Does it even try to boot? You say it emits a beep, what kind of beep exactly? Beeps are used to inform of errors that happen before the display has been initialized.

Quick, short one - the kind you'd hear on passing the POST. I've connected a floppy drive and inserted a DOS boot disk - the computer does a floppy seek test and proceeds to load something from the floppy.

Was the board dead before you swapped the caps, or was it just done to be on the safe side?

Have you tried a fresh battery with a cmos reset?

Have you checked the jumpers are set?

If you think it might be completing a boot to DOS, stick a line at the end of the autoexec.bat file like 'dir > a:\dirchk.txt' and check this txt file exists on another working machine

However, this link suggests a possible memory refresh failure http://www.uktsupport.co.uk/pb/mb/amibeep.htm

Yes, the board was operating before capacitor replacement. The caps were in really, really bad shape and the 2 big ones had already bloated, so there was no point in waiting on a disaster. Fresh new CMOS battery was also installed. All the jumpers have been set accordingly, to a non-overclocked Pentium 133. BIOS password is not an enabled function on this board - J4K2's Password Clear has been left as was.

I managed to boot up the board once, though. I posted on Tom's Hardware and a user mentioned how the behaviour of the system on boot-up was identical to a "BIOS recovery mode" used on updating the BIOS. That's why it reads from the floppy - it seeks for a flash file.
He suggested checking the jumper, and what do you know - one pin was corroded and split in half, and the jumper's insides had corroded too. I managed to bridge two of the pins with a screwdriver and shift to a "normal operating mode" and the display lit right up. Then the pin broke off completely 😒
I ended up replacing the whole 3-pin thingy with some spare I found. Soldered up and everything is right... except that now I get that classic "blank screen, no beep on POST" situation. Interestingly though, when I switch the jumper to the recovery mode again, the PC's behaviour is back to what I described - blank screen, one beep, attempting to read from floppy.

What do you reckon, what's most often the cause of that no-POST boot?

Maybe the BIOS was damaged? Can you set it back to BIOS recovery mode and reprogramm the EEPROM?

Sure, there is a procedure to re-flash the rom with an updated one by going to the recovery and inserting a floppy.

I don't really think this is the problem, though. Perhaps it's something of a bad/improperly inserted memory, or something. Will try that before I do any BIOS flashing.

would it make a beep if u had bad sticks of ram?

Yes, it does make a low, switching buzz. My guess is the BIOS can't be damaged since when shifted into recovery mode, it behaves like it should.

I should clarify - after getting that bit of advice on the jumpers, I did manage to boot and POST succesfully once by shorting the pins into the "normal" boot position. It was only after I soldered in the new jumper holder thing that this behavior came up. I reassembled it in a skeleton configuration, that is only RAM, CPU, and CPU fan, onboard graphics, no riser card. What bothers me the most is why does the "recovery" boot procedure go as it should, yet a normal boot results in a typical blank screen without any beeps.

Update - changed one jumper, the Password Clear jumper, back to the "clear/disabled" setting. Focused on the RAM sticks - maybe one of them is bad. All I get is 3 low-tone buzzes on recovery mode - on normal mode the computer stays dead and silent. I have a AMI BIOS - according to a cheat sheet 3 short beeps mean "base 64K memory failure". No word on what tone, though.

In case anyone's wondering, yes I am using a ESD strap, and disconnect the PSU and ground myself after each powerup before I start removing any parts.

(edit) Just removed the riser card with the ATi card, installed both sticks of ram in Bank 0 - recovery mode is back as it was, no video nor beep in normal mode though.

(second edit) Installed the PC in the case, downloaded a flash utility from vogons file database - it completed the flash, and we have a POST screen. I guess all I had to do was shove it in the case - maybe the board needs ground from the case, or something. Topic closed, thank you.