Well, it started to happen two days ago (suddenly - I didn't do anything hardware related with the computer).
What my computer does: Sometimes it reboots fine, but sometimes it simply stops working instead of POST and Windows start. The monitor turns off and that's all - even after rebooting using the case button. After turning it off (including PSU) and back on it's the same - all HDDs and fans spin up, CD/DVD drives work as usual even the Q-Fan slows down the CPU fan, but the monitor stays off and nothing is happening. It takes a few on/off cycles for the computer to succesfuly POST and start Windows.
Clearing the CMOS didn't help - it posted but after I saved the default BIOS settings and rebooted it was the same again.
I suspect that it is the motherboard problem, because I experienced a similar problem a few years ago with a 430TX mobo - I had to replace two capacitors on it (and it works fine since then). I didn't find any weird looking capacitors on my P4C800 though.
I'm afraid to reboot or turn off the computer because I don't know if it will start again. And I need it because I have a lot of work to do now.
...but I guess I'll have to turn it off anyway to try to reseat all components.
Any suggestions? I'll do some more investigation meanwhile...