I have the exact same problem as josh.
I'm a complete computer novice so forgive me if I cant understand stuff.
My PC worked fine until I tried to directly switch it off by long pressing the power button at the front of the case. The computer went off but I couldnt put it on again through the power button. The PC starts automatically as soon as I put on the main switch on the wall. The fans turn, the hardisk spins, the cd in the drive spins but after a few seconds it all just goes off.
I've unplugged and plugged everything, cleaned and put back the heatsink, tried checking if it stays on without the cd drive/ram/hd(doesnt work with either of them unplugged)
The funny thing is that sometimes just like that it starts working fine. Just yesterday when it was not working, I slammed the cabinet really hard with my hand and when I put on the power it started working.
Another thing is that once it starts running it gives me no problem whatsoever, even rebooting doesnt cause problems, but once i shut down my PC it starts giving this problem again.