Are you getting any beep codes ? Is the "640k installed" kind of message appearing before this?

Try unplugging the disk drives. If no drives are detected, it should default to booting into the DeskMate ROM.

Drives are still hooked up and I don't hear a beep.
It immediately goes to this screen.

Maybe the EPROMs suffer bit rot (data corruptiion) or some connections aren't good.
I'd remove the chips from their sockets and clean them using isoprophyl alcohol or purified/destyled water and an tooth brush.

Or something else that's aproppiate. There are so many cleaning tips around (better double check). 😀
In some cases, warm soapy water also works fine, I heard. Anyway, these are just ideas.

Normally, I'd recommend a POST card (diagnostic card), but..
I don't know a lot about the Tandy 1000. It was rare in my place.
No idea, if it can produce POST codes at all.

It's probably best if another Tandy 1000 user can land a helping hand.
It's a wonderful machine, but also very specific in its design.

Edit: Some typos found and arrested.

Oh yeah I forgot about my POST card: I also don't know if it will work but it's worth a try!
Currently I am removing the chips and cleaning them but it might take a while since I have to do it in small timeframes.

I'd try to eliminate the possibilities. If unplugging the drives makes no change, I'd check to see if it has a coin type battery somewhere. If that failed, I'd see if it had one the Dallas rtc chips, and unplug that. Beyond that, the ram chips are about it for replaceables. I know they came with 384k standard, and were plug in chips, but I can't remember if all or only some are replaceable.Have you tested the PSU to make sure the voltages are good?

I am not up to that level of diagnosing yet. I've been planning on buying a multimeter for quite some time but I've never gotten to it to be honest. I should make work of it.
Floppy drives have been removed but made no difference.
Tandy is unknown for me but afaik there is no coin cell or Dallas RTC on the board. It uses an optional Tandy Smartwatch RTC chip.

Just putting this here in case you're not aware of it; it's the best Tandy site I've found in my travels.

http://www.oldskool.org/guides/tvdog/1kfaq.html

I stumbled on it this morning 😀
But thanks anyway. Going to buy a multimeter too now. Always handy...

OK,so I reseated and cleaned pretty much all the chips except 1(a Zylog one).
When I turn it on now, I see 640k ram and then it goes to the blinking garbled screen again.
Is this a RAM problem or EEPROM or.....?

No Tandy experts here 🙁??
When I remove the left bank chips, I get 384k RAM instead of 640k and after that, again the blinking screen.
When I remove the right bank, I get that garbled line like when I remove them from both banks.

Removing the EEPROM and letting it sit for half a day on a iron flat surface did nothing.

Could the problem be in the soldered on chips? I don't want to order 16 new RAM chips and still have the same problem.

I tried an Trident 9000i (3 jumpers set to 8 bit according to the manual) and an ET4000AX (2 jumpers which I don't know what they do) but no signal to the monitor.
I can test/try 1 more thing and that is to replace the Video/Interrupt jumper from E2-E3 to E1-E2 (still need to look up what that does exactly because I read somewhere the SL should accept a VGA card without having to change something).

Had another idea but it failed yesterday. I removed the chips from the left RAM bank and used 4 to replace U6,7,8 and 9 which seem to be used for video according to the service manual.
Still the blinking screen.
Inserted a Hercules card: still the same.
Removing the 4 chips gives me a non blinking screen with smileys and other characters. Not garbled too.
I ordered replacement DRAM chips but it will take a while.

I think I read somewhere that using an ISA card should solve the problem if the problem was with the video ram but as stated before, the Hercules card didn't change a thing.
I have no 8 bit VGA cards too, only a TVGA9000c and 9000 i. Putting them in 8bit mode (according to jumper markings and Stason), doesn't do anything. I get no image on the screen.

No Tandy experts here 😀?

Tandys use a weird mapped video memory that is 'borrowed' a bit as I recall. Some noticed it causes the machine to display a 'wrong' amount of memory depending on what's installed and what the setup was, iirc. I'd expect the 1000sl to work with EGA or CGA better than VGA. Tandys graphics are roughly analogous to EGA. Can't remember, is there also a coin battery on that board? Scour it good, just in case. I'd also try removing the rtc chip, they can go bad as well.

Yeah, some RAM is borrowed for the video. Hence using a VGA or other card should bypass it.
I can try taking out the CGA card from my 5160 but VGA shouldn't be a problem. Except it is now since my Tridents don't give an image.
Some of my other systems have ISA cards too but I don't want to open them all to test :p
My ET4000AX didn't work either but not sure if I set the jumpers correct.
The 640K RAM is displayed perfectly but the next step is the blinking.

There is no RTC installed. It's an optional Dallas chip.

I hope the new DRAM fixes it but if not, I'm running out of ideas. Could be the EEPROM but then I will need to disassemble my working one and remove the EEPROM there.
There is a "fix" I read about connecting pins 4 and 8 when booting but that is for the RLX and I'm not sure it works on other types.