Mine keeps starting back up ramdomly.
It sometimes shutsdown and restarts straight away and sometimes it does not, but I can leave it off and then eventually after a random length of time, I will go and the there!
Sometimes Its kind of hung just after it displays the PRESS DEL FOR BIOS, it seems to hang there or it gets to the desktop.
Sometimes it fails 3 times and goes into the BIOS anyway and then it starts up normally.
Irritiating thing but when its running, its flawless.
I leave it on 24/7 so its not really annoyed me too much.
On the Faulty GPU point, I have tried batter cards, both ATI and nVidia and they all have some issue. But right now, I am using old ATI 7770 cards and its flawless. It could be that the GFX slot is playing up, cos those cards work great in other PCs.