It seems the board has lot of corrosion, several of the vias on the photos look like they're no longer conducting. It would be possible to revive this board but it'll take a lot of work.

Hmm... If I was asked to fix (or try to) this board, I would also try the diagnostic card to see if there's any activity. The fact the board doesn't beep doesn't necessarily mean it's totally dead. I would also inspect (and eventually replace) all sockets that might get into touch with the corroding fluid. However, the chances to fix this one aren't too high. There might be some corroded trace under the CPU socket and removing it and fixing the broken traces would be too much of effort. The same for the chipset chip. Also the vias might be damaged.
While fixing Commodore PC-10's, I've also noticed that corrosion sometimes somehow gets into the chip itself - the memory chips next to the battery were all dead, while the memory chips farther away from the battery were all good. If the fluid got into that chipset...
I'm also surprised about the location of the corroded traces - did it have an external battery positioned over the board? Or where did that corrosion come from?

This board sat in an uncovered box in a shed for a long time and was covered in dust. I think the corrosion is just from being exposed for so long and condensation from moisture in the air. I don't think anything has spilled on it.
The other boards in the box were all fine, just not this one which was on top...

Then it depends on how much effort do you want to put into it 😀 Similar working boards just sold on eBay.de with CPU and memory in range from 30 to 40 EUR.
Anyway, if you still want to try, I'd recommend to try that diag card first. I've tried some and I can recommend this type: https://www.aliexpress.com/item/4-Digital-LED … 2860150439.html . Others I've tried didn't work at all, or didn't work reliably. If the card shows something, it might give you a clue of what you should do next.
While waiting for the card, try to reseat all the chips, especially the BIOS one, and check the socket and chip pins for corrosion. Replace socket if in doubts. Remove the cache, check the jumpers. Give the whole board a good wash in slightly soapy water, and use soft brush (preferably antistatic), rinse with demineralized water and let it dry well (few days, and on the sun if possible). If you do have an EPROM programmer, try to find working BIOS for the board and compare it with content of EPROM (EPROMs tend to lose content, especially in higher temperature environment).
Try a VGA card and see if it does something - and try all ISA slots (the ones next to battery tend to be dead sometimes). If you feel like that, check all the traces for continuity, including vias.
By the time you finish this, you will either have a working board, or a hateful relationship with it 😀
BTW: do the other boards work? Perhaps it was just a pile of junk and you're trying to resurrect something that has been dead before already.

That pretty much meets my criteria for "lost cause" 🤣

I agree it's not really worth it... I just thought I'd see if anyone had had success restoring a dead board this with a can of PCB cleaner, in case it's worth a try. Even the cost of that isn't really worth it unless there's a high chance of success.

Yes all the other boards worked fine... but this one also had all the jumpers removed, so you may be right, maybe it was already known to be dead. (Some of the other boards had jumpers removed too though, so who knows...)

PS - thanks 😀

I tried one of those diagnostic cards (same as your link) - the reset LED lights continuously indicating a fault with the reset circuit... as if the reset button is pressed in all the time I guess, which is consistent with no beeps.
I'm assuming that wouldn't be an easy fix, if even possible. But maybe a more thorough clean would help, who knows.