Asus boards from that era tended to have better than average caps, but after 25 years any electrolytics are suspect. Check the DRAM voltage actually delivered (with a multimeter). If that's well below 3.3V you have your cause and main culprit for that is the caps helping regulate that voltage.

Thank you for your advice. The board has Rubycon YXG, one of the best I've seen on the boards, all seems to be in good condition. I measure mosfet next to ram slots and it has 3,3V so I think problems with RAM supply is not in suspicion.
But the case gets more complicated: I tried the board again, now with AGP card and the POST code changed to F4.
After fitting an even different PCI VGA than yesterday, the code changed again - F0. So I don't know if it's possible to take the results of a diagnostic card seriously.

I measured the mosfets in the VRM for the CPU and I measured 0V on one of them - that doesn't seem right. Could this be my problem?
The board has a Pentium III 800, which should have a Vcore 1.7V, which I can't measure on any leg of mosfetes.

Ydee wrote on 2022-11-21, 09:10:

I measured the mosfets in the VRM for the CPU and I measured 0V on one of them - that doesn't seem right. Could this be my problem?
The board has a Pentium III 800, which should have a Vcore 1.7V, which I can't measure on any leg of mosfetes.

0V- OK, it's GND rail.
1.4V is Vcore before a coil, I think it is not OK for Coppermine. But it's better to measure Vcore after the coil of CPU VRM and compare.

P.S. Stops at different debug codes may point out that some voltages are wrong and system just hangs randomly

Thank you for the valuable advice, I measured the coil in phase and the voltage behind it is really 1.69V. So Vcore's voltage is probably fine, too.
Then I'm running out of ideas. I don't know the history of the board and if the damage is somewhere between the PCB layers or under BGA, I have no way to fix it. The board has an Award BIOS (aka Medallion by Asus) and the codes F0 and F4 are not explained at the Award.
Moreover, I don't know if the POST card gives the codes correctly - the beeper on the board doesn't react at all (it doesn't beep). However, I cannot guarantee that it is functional.
Too bad, it could have been a nice little microcase board.

Ydee wrote on 2022-11-22, 08:22:

Thank you for the valuable advice, I measured the coil in phase and the voltage behind it is really 1.69V. So Vcore's voltage is probably fine, too.
Then I'm running out of ideas.

It's difficult to say about quality of voltage just using a voltmeter.
I had similar problem with MSI P45 mainboard. It hung randomly at different POST codes. All capacitors looked ideally. But when I desoldered one and measured its ESR with an ESR-meter (cheap one from ali) the ESR appeared too big and capacitance - too low. All they were faulty that caused instability of RAM voltage. Recapping solved the problem.

Of course maybe it's not your case.

P.S. Try to check correctness of settings of DIP_SW and maybe set minimal FSB (66MHZ) for an experiment matter.

try with no ram and graphics, and as Roman555 said at this point in time (~2000) you have to use oscilloscope to check if voltages are correct - looking for sags, spikes, noise, ripple.

Thanks for help, friends. I'll have more time this weekend, so I'll try to look at it again, but I don't hold out much hope. I'll flash the BIOS again if there's a problem with it, but personally, I don't think so. Unfortunately, I don't have the equipment or knowledge for more detailed testing (I'll flash the hotflash method because I don't have a programmer or oscilloscope to compare voltage patterns), so my options are strictly limited.

I tested the board with dip settings on jumperless mode, I'll try manually setting the frequencies again and see. I will also test without RAM and VGA if the card responds with other codes.