Sounds like a faulty power-on reset circuit.
Possibly something up with one or both of the two transistors involved in the circuit, though without a schematic for the G2 chipset I cannot say with any degree of certainty which parts to check/replace.
Or maybe an open resistor in the circuit, but that's somewhat less likely.

But, simple checks first. Does it do this when you remove the other cards?

cabbagelord wrote on 2021-09-30, 15:40:

Checked with a "POST card" with two alphanumeric displays

The POST card should have one LED for reset line on ISA bus. This signal usually comes from the chipset but follows the global reset. See if you get a slight delay (300-1000 ms) between power-on and this LED changing state. If the delay is too short, it's quite possibly the PSU generating out-of-spec POWER_GOOD signal. The mobo might not have fully started up yet (clock generator(s) usually). Modern PSUs keep this delay to minimum so if you are using ATX to AT adapter it could be because of that. On older PSUs dried out caps can lead to this delay being too short.

Oh, and if there doesn't seem to be any delay, and you've tested more than 1 PSU, it's quite possible the POWER_GOOD signal trace is broken. It usually is a thin one and routed close to the battery, a spill or corrosion can easily take it out. By default a pull-up resistor will keep the mobo out of reset if that connection is broken, but there won't be that initial reset pulse on power-on obviously.

Thanks @Deunan, inspected the power-on circuitry and found a broken capacitor.

Replaced C1 with a ceramic 100n capacitor. Everything works.

R1 = 10Ohm, R2 = 100kOhm

100n capacitor was not enough seemingly, as after a week when I tried to start the motherboard, it didn't start.
Replaced with 1uF electrolytic (later intend to replace with ceramic one)

Keep in mind modern ceramics of that capacity are almost always MLCC - and these are especially susceptible to capacitance drop when charged. So assuming a 6V3 cap, and targeting 1uF, you should probably put a 2u2 in there (yes, a 50% drop is not unusual close to rated voltage). Frankly this is a perfect place for electrolytic, 10V or 6V3 one would stay formed due to being at 5V all the time and you do not care for ESR one bit, it could go to 100 ohms and it wouldn't make any difference. But if you need it to definitely outlive you (especially if that mobo is in a hot spot or something) then ceramic or tantalum would be better.

Also keep in mind that many microelectronics require some minimum reset time/cycles in reset state.
This is necessary for example to properly clear out internal registers, memories etc and set them into a defined state.
So, in practice it is good to have a reset time constant of one or two seconds.

Deunan wrote on 2021-10-08, 20:35:

Keep in mind modern ceramics of that capacity are almost always MLCC - and these are especially susceptible to capacitance drop when charged. So assuming a 6V3 cap, and targeting 1uF, you should probably put a 2u2 in there (yes, a 50% drop is not unusual close to rated voltage). Frankly this is a perfect place for electrolytic, 10V or 6V3 one would stay formed due to being at 5V all the time and you do not care for ESR one bit, it could go to 100 ohms and it wouldn't make any difference. But if you need it to definitely outlive you (especially if that mobo is in a hot spot or something) then ceramic or tantalum would be better.

Thanks!
I mainly source my components from AliExpress, so opting for an electrolytic capacitor is dangerous to the board and a ceramic cap seems to be a far safer choice.

Thanks a lot for pointing out the MLCC bias voltage issue. I have ordered a bunch of 50V 1uF so this should not be an issue as long as they would stand by the label.