Here's the problem:

When I start the PC, the mainboard powers up, then stays that way maybe 0.2-0.5 seconds, and then shuts off again.

I say mainboard, and not PC, because I removed all the parts from the system and disconnected everything but the mainboard power supply (the broad 12 pin thingy).

When I have the other parts (cpu, graphics card, ram, etc.) installed and connected, the basic behaviour stays the same, but now the mainboard runs for about 6 or 7 seconds (this is a guess) before shutting off.

This all started when my monitor wouldn't receive a video signal today, without giving POSTs, so I took the graphics card and the RAM out to see if it changes anything. It didn't, except that from that point on the mainboard would start to have this behavior where it just stays on for a very short time and then shuts off again.

I already tested it with a backup PSU -> same behavior.

What could this be? I'm thinking it can't be on a physical level (transistors burned through or something like that), since then the mainboard either shouldn't start at all or it should detect hardware failures in non-essential parts of the syste and start beeping.

Sorry, I forgot to mention. It's an MSI P67A-C43. I already checked the capacitors if someone popped, but I can't find anything. I also tried resetting the cmos, but that didn't change anything.