Bulging/leaking caps?
Tried underclocking?
Given it a good wash?

Thanks for chiming in!
There's one bulged cap next to the CPU. So, I should recap the board before giving up on it.

Apple][ wrote on 2024-12-21, 18:32:

Thanks for chiming in!
There's one bulged cap next to the CPU. So, I should recap the board before giving up on it.

Absolutely! This is actually good news, as a component that has visibly failed makes troubleshooting much easier. At the very least replace the one, and if it were me I'd be sure to replace all of the same brand/capacitance that failed as well.

You might not have to recap it to make it work enough to boot.
Set the fsb/mem to the lowest it will go and multiplier to 2 and try again.
If it works, it's worth recapping.

Well, it was worth trying.
K6-2 350 got to POST at x2.5 multiplyer; K6-500 at x2.0; bus/mem freq. 66 MHz.
It didn't boot with the same outcome.

These caps definitely don't look good though:

Apple][ wrote on 2024-12-22, 03:42:

Well, it was worth trying. K6-2 350 got to POST at x2.5 multiplyer; K6-500 at x2.0; bus/mem freq. 66 MHz. It didn't boot with th […]
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Well, it was worth trying.
K6-2 350 got to POST at x2.5 multiplyer; K6-500 at x2.0; bus/mem freq. 66 MHz.
It didn't boot with the same outcome.

These caps definitely don't look good though:

The attachment caps.jpg is no longer available

Looking at the photo, I would change all three, even if one seems fine, actually measuring it, it might not be like that, and if you have enough spare, I would also look at the others present on the motherboard, and I would also replace those equal to the three (if there are others), if it continues to manifest the same problem after changing capacitors, you have to continue to change the remaining ones, if instead the problem disappears, you can start the celebrations 🎈 🥳

Thank you for the support.
I'm expecting my new ESR tester to arrive on Monday. Then I'll check all capacitors and will order a bunch from Digikey.

Unfortunately an ESR meter will be fooled by capacitors in parallel to the one you're measuring - so they have to be removed to be tested, at which point you might as well just replace it anyway.
But if the meter shows a high reading in-circuit, then you'll know you have a problem with every cap in the circuit.
If only some of the caps in the circuit are bad, the others will follow anyway because they're probably all the same. As caps fail, the working ones take on more stress which can accelerate their demise.

If you see (or feel) any amount of bulging then the cap is very bad. Those symptoms don't always appear at all. When they do, it's after the cap has been dead already and is severely out of spec.