I would start by unscrewing each mount point one by one and testing. I have a 486 which wouldn't even post because either something would short to the chassis, or the board is maybe slightly warped, or something else; worked perfectly fine outside the case as well. Never really figured out the root cause, so I just leave that one mount point empty, and it's happy as a clam.

Here are a few pictures of my computer case. If I install this in the computer case, the PC freezes, if I start the games with the sound effects turned on with only midi sound the games work fine

Once my sound card would intermittently work on and off, then it started to happen with other cards. Finally I realised the case was making the card not fully touch inside the end bit of the isa slot. Looking from the top it looked fine but from close in a certain angle I finally saw the contacts were not making a good connection and gaping a bit

egbertjan wrote on 2022-12-18, 22:58:

When I built this in the case the system crashes when I play DukeNukem 3D with all the sound-effects. With just the midi it works OK. The same occurs with other games like HighSeas.
When I build the system outside of the case everything works OK.
Beside this there is also a problem with the connector of the com-port. When I screw the connector on the case the port doesn't work. It works OK when I connect the mouse to the port without srewing it in (on) the case.

Sounds like a ground issue. Could be a short when mounted in the case as mentioned but the Com port mouse thing makes me think maybe you are using the wrong com port dongle or some other thing is up.
Technically the metal bracket of the com port AND mount holes of the motherboard should be same ground as the case if wired proper. Are you using an adapter from PSU to motherboard ?
I suggest checking the voltage of the Com port mount frame (when not screwed in) to any ground point of the mother board to see if is actually ground and 0.0 volts.
I also suggest checking the ohm's from Com frame to motherboard ground with PSU disconnected.
added: worse case scenario: your PSU is the issue with a floating ground....just some thoughts...

I use an adapter between the motherboard and the power supply

I use this adaptor