I've got GOOD NEWS and BAD NEWS. First the good news...you're not alone! And now for the bad...I don't know to solve this problem....
When I read your post, I suspected that you had an ATI Rage video card, because I have the ATI Rage Fury PRO, 32MB AGP and mine does the same thing...it's almost as if the card overheats and just shuts down. When it happens, the monitor shuts off, just goes black, with the little white dot in the center as would happen if you pressed the monitor's power button, but the monitor lights indicate that it's still getting power. No amount of fiddling with the keyboard, e.g. Ctrl-Alt-Del, Alt-Tab, Escape, Windows Key, et.c etc. etc. will help. The only recourse is to shut the system off and start it up cold.
The only difference between our situations is that my system button works, as long as I hold it in for 5 seconds, while yours doesn't (there is an option to select what the power button does when you hold it in. I can't remember where the option is, maybe in Control Panel>Power Management??, but one of the choices is to shut down, while the others are Sleep Mode, and Suspend...or something like that. I suspect your's is set to go into sleep mode or suspend instead of to shutdown.) In my case, there isn't one program that causes it to happen, it just seems to be more prevalent if I leave it on for a day or two, than if it's been shut off recently (hence my comment about possible overheating).
While I can't offer any suggestions for solving your problem, I would strongly suggest that you make sure there is NO Harddrive Activity when you unplug your system! BEFORE you touch the power cord, check the lights on the front of your computer tower. The Harddrive access light (I believe it's the orange one...??) MUST NOT be flashing. Shutting it off while it's accessing the harddrive will eventually lead to damaging the harddrive permanently, so be careful.
I'll be following your thread with great personal interest. Just FYI, I have the latest drivers installed and I know a little about computers considering I built this one from scratch (AMD Duron 750mHz, 256 mb Ram, ATI Rage Fury Pro 32mb AGP, SoundBlaster LIVE! X-Gamer, etc.)
GOOD LUCK! Darren.