You'll forgive me if I don't recall all of the specs on this computer, I first built it 6-7 years ago and have since replaced / upgraded many parts (gfx card, motherboard, processor, ram). I think the only thing original in the computer is probably the 2 smaller HDDs, the dvd drive and cdrw drive (currently disconnected - no power / no ide).
Asus P4V8X-MX motherboard
NVidia 6600 GT
2x 512mb ddr
450 or 550 watt psu
40, 80 & 300gb hdd's
Using on-board sound.
The problem started about 9-10 months ago where it would randomly freeze upon usage. When rebooting I would get no display, no bios and no beeps. To fix this I typically would reseat / push down on the processor, ram, cards & drives, to make sure everything had a firm connection. This was only a temporary fix and the computer would crash anywhere from 10 minutes to 48 hours after a boot. It would also freeze/crash while either under strain or when not in use / idling.
Then it stopped and hadn't occurred for the last 8 months... until Sunday where the same issue and same scenario has been playing out.
I've looked around here and seen people with some similar issues and the common suggestion has been to replace the PSU. However, the fact that this problem occurred, then stopped happening for such a long period of time leads me to believe that it could be something else. This PC is essentially a media computer that typically gets rebooted once a week or once every other week.
Could be a dead fan. If spins slowly or has stopped and now something is overheating because of that (around 8 months ago sounds like middle autumn and now it's getting warm again). Check temperatures, rpms, voltages.
How old is the OS install? Maybe you should reinstall (not an issue if you have linux).
Possible, it could also be that your capacitors are going on your motherboard and or power supply, they do get old and die, especially from 2002 or so, and it can have all kinds of strange effects such as random crashes or not powering up, rebooting....