First: pictures always help ! Picture of the EGA card and motherboard front and back.
Did you test the known good VGA card in multiple ISA slots on the 286 ? Did you test the 286 PSU ? The short could have caused an older PSU to partially fail.
If you short a +V supply in ISA slot it can take out traces you may not be able to see....

Added: One of my top rules: Never test a newly bought card in a board that you value, always use some throw away/test board you do not care much about.
Yeah some do not have a large collection or an old ISA based board they can do that with but over time you learn that some cheap board is a better test bed that putting in a good fully working system and risk ruining it....

Some video cards need +12V for the clock circuits, card will not work without it. Both + and -12V migh be needed for RAMDAC but that would just cause the screen to be blank or barely readable, but not beeps.

First thing to check would be if there still is 12V on the ISA slots (test all of them in case the trace got burned on the mobo). If all voltages are present and in spec try a different slot, these early 286 mobos can be really picky about that (and video cards, seems not to affect other ones much).
As for original EGA card, if the copper hasn't overheated due to short just replace the cap. Old tantalum "teardrop" caps can just short and catch fire on their own (case cracking due to mishandling or just heat cycles and moisture/oxygen getting in). Replace with 25V rated tantalum if it fits, rather than 16V one that was probably in there. Perhaps also replace any other 16V tantalum caps on the +/-12V lines while at it. However if the 12V line on the card is damaged you will most likely need to patch that, also a simple job with a piece of wire but doesn't look as nice. Better than non-working card though.

Thanks for getting back to me! Yeah I've definitely learned my lesson here regarding newly acquired hardware.. This has never happened to me before, so I didn't even think about the possibility aside from old PSUs were I had heard that those can be problematic.

I believe the PSU is still fine, as I also used it to power a different board in order to verify that the VGA card is working. But I will also try with a different PSU just to be sure.

I've tried the VGA card in two different slots so far, but not all of them, I'll do that as well.

Pictures of the board:

The blown up cap (I already removed it from the card, since it smells horrible):

The two solder points where the cap used to be are connected to GND and +12v - maybe that's already an indication of a short somewhere else on this card? Or does it make sense for a cap to just sit directly between power and ground?

I'll post pictures of the card next (can only do 5 attachments per post)

And here's the card:

Close up on where the blown cap used to be:

These tantalum caps only do local power plane filtering, so they sit between various voltage rails and GND (and usually the rail is routed with a pretty thick trace so that shouldn't really burn easily). There is a very good chance all that is needed on that card is a new capacitor, and in fact it might just work without it (but can be unsable or have more noise in the video output).

Frankly I would clean that EGA, by my standards it's filthy. At the very least brush it (a soft wall painting brush is great for that, make sure it's new and clean or clean it first). I'd even give it a good bath but it does have some paper stickers, so you might not want to. Take the metal brace off and clean the blown capacitor area well (q-tips and some 70%+ IPA), the smoke residue it left can be somewhat conductive and you don't want 12V in places it should not be present.

Inspect all the other tantalum caps, replace any that show deep scratches or craking. You could go with aluminum electrolytics instead but these do age, tantalums do not (but the early ones catch fire as you can see, mostly due to abuse but some can just crack on their own - and these cracks can be tiny and appear between leads where you can't see it).

lethal_guitar wrote on 2021-10-05, 09:26:

The two solder points where the cap used to be are connected to GND and +12v - maybe that's already an indication of a short somewhere else on this card? Or does it make sense for a cap to just sit directly between power and ground?

That's sounds right, that capacitor would have been smoothing the +12V supply so that it stays a fixed voltage away from GND.

It's probably nothing, but on the motherboard there are 3 capacitors at the top of each slot for +5, +12 and -12. On the back there's what looks like a bit of bubbling on the 12V track just where is goes past what I think is the GND leg of the +5V to GND capacitor for the furthest slot. Check that there's no low resistance between the +12 and GND.

Given you've already had the board on, then it might be worth checking what the voltage is on the B9 +12V pin for each of the slots.

[edit: Oh, there's also something that looks like some corrosion going on under that 7406 U14 near the 286]

Ok great news, turns out the board works fine it just doesn't like the VGA card in any of the top two 16-bit ISA slots, like some of you mentioned. If I use either of the two bottom ones, it boots up and works fine! I must have only tested the upper two after the cap popped on the EGA card. I feel a little dumb now 🤦‍♂️ But many thanks for all your suggestions!

snufkin wrote on 2021-10-05, 10:07:

That's sounds right, that capacitor would have been smoothing the +12V supply so that it stays a fixed voltage away from GND.

Ok, cool - I still don't know a lot about the analog aspects of electronics, so never sure with things like capacitors and resistors.

snufkin wrote on 2021-10-05, 10:07:

It's probably nothing, but on the motherboard there are 3 capacitors at the top of each slot for +5, +12 and -12. On the back there's what looks like a bit of bubbling on the 12V track just where is goes past what I think is the GND leg of the +5V to GND capacitor for the furthest slot. Check that there's no low resistance between the +12 and GND.

Fortunately, it turned out that these two spots you see on the photo were just little pieces of foam from the foam mat I had put the board on. I've put it on top of some ESD foil instead now, to avoid more foam pieces getting stuck there.

I did also check all the voltage rails on all ISA slots, and they were all fine. So it's all good in the end, now I just need to clean up and resurrect that EGA card. Thanks again for the help everyone!

That is good news ! Great ! Side note: Have found some older ISA boards do not like 16bit cards in certain slots, just like you found. Not sure why but it does happen 😀

lethal_guitar wrote on 2021-10-05, 14:55:

Ok great news, turns out the board works fine it just doesn't like the VGA card in any of the top two 16-bit ISA slots, like some of you mentioned. If I use either of the two bottom ones, it boots up and works fine! I must have only tested the upper two after the cap popped on the EGA card. I feel a little dumb now 🤦‍♂️ But many thanks for all your suggestions!

This is where I would get the contact cleaner out and go over those 2 top slots carefully, cleaning dirt and corrosion, and checking things over.

There is no good reason why the top slots wouldn't work while the 2 bottom ones do.

canthearu wrote on 2021-10-05, 23:55:

lethal_guitar wrote on 2021-10-05, 14:55:

Ok great news, turns out the board works fine it just doesn't like the VGA card in any of the top two 16-bit ISA slots, like some of you mentioned. If I use either of the two bottom ones, it boots up and works fine! I must have only tested the upper two after the cap popped on the EGA card. I feel a little dumb now 🤦‍♂️ But many thanks for all your suggestions!

This is where I would get the contact cleaner out and go over those 2 top slots carefully, cleaning dirt and corrosion, and checking things over.

There is no good reason why the top slots wouldn't work while the 2 bottom ones do.

I have a few odd boards that do that and cleaning did not help (maybe cold solder joints??), one being PCI that refused to work with any PCI vid card in anything but the closest slots to the PSU connectors. Makes me wonder if some traces were purposely not run the full board but never checked or some odd BIOS thing.

Horun wrote on 2021-10-06, 00:00:

I have a few odd boards that do that and cleaning did not help (maybe cold solder joints??), one being PCI that refused to work with any PCI vid card in anything but the closest slots to the PSU connectors. Makes me wonder if some traces were purposely not run the full board but never checked or some odd BIOS thing.

I've had to replace multiple PCI slots on one motherboard (Athlon Slot A) because the slots themselves were bad.

I do have another P3 motherboard that has a defective PCI slot as well ... no idea what is wrong with that one, even replacing the slot didn't fix it. Will buy an oscilloscope and try to fix it one day!

But yeah, ISA cards are just logically connected in a line with each other. They don't get individual signals at all, so OP should be able to diagnose what is different between the top and bottom 2 slots and fix it.

canthearu wrote on 2021-10-06, 00:10:

But yeah, ISA cards are just logically connected in a line with each other. They don't get individual signals at all, so OP should be able to diagnose what is different between the top and bottom 2 slots and fix it.

I can look more into it, but it sounded like some 286 boards simply behave this way based on what Deunan was saying:

Deunan wrote on 2021-10-05, 08:50:

If all voltages are present and in spec try a different slot, these early 286 mobos can be really picky about that (and video cards, seems not to affect other ones much).

I did already check all the voltage supply pins for all ISA slots, and they were all fine. I can double check all the other pins and see if I find something

A reasonably quick check would be to do a one-to-one continuity check between a working and non-working slot, going down all the pins.

It probably is just a dirty contact, but I wonder if the slot pickiness could be some sort of bus termination issue. I assume the bottom two slots are the two nearest the edge of the board, so at or near the end of the bus where any ringing is going to be only fractionally behind the actual signal, but the top two slots are in the middle, so maybe reflections from the end are delayed enough to cause problems. If you put a card in the end slot will the video card then work in one of the top two slots?

It has to do with signal integrity. Now, this particular mobo is single-chip solution and does seem to have resistor packs to load/terminate the ISA bus - so any card should work in any slot, in theory. It could be some broken or weak trace between slots, or dirty contacts. But then again it's 286 mobo and these do have their quirks, no matter how modern they seem, so it's best to try all slots - especially with video cards. The faster the card the more issues it will have with signal timings and/or reflections.

I finally had time to look into this again, and I have a question I was hoping someone could help me with. I've ordered some replacement caps but now I realized that these have a tolerance rating of 20%, whereas the original caps seem to have 3% (the only marking on the caps aside from polarity is "106H", and it seems that the H denotes a tolerance of 3%).

The replacements are also a little bit thinner/less bulky than the original ones.

Side by side:

Does the tolerance matter in this case, where the caps are doing power line smoothing? From what I'm reading so far it might not really matter if the caps aren't part of some actual signal path but the difference between 3% or 20% seems quite large to me.

I also briefly tried finding tantalum caps with a narrower tolerance rating but couldn't find any so far.

it's fine quit over thinking it

I'm happy to report that after recapping, the card is working flawlessly! And visually, the new caps fit in much better with the rest of the components than the orange ones did, imo 😀

Thanks again everyone!