Just a thought, Check and verify that both the fans on your GPU itself are functioning properly. My friend had a twin frozr 5770, and it started overheating and crashing very quickly, and we found out that not 1, but BOTH of the fans on it had completely seized up and could no longer spin. I ghetto rigged a couple stock CPU fans onto the heatsink of the card and it works flawlessly.
You so lucky! Just one of the fans on one of my 560's died and the card went up in flames.
What's weird, is he pulled the card from his friend's working computer, and we installed it into my friend's new pc immediately afterwards. The pc would run for maybe 1 minute tops before a very high pitched continuous beep would go off and the screen would go blank. Looked at it, and saw both fans move slightly but not spin when the power button was pressed. In fact the fans had a lot of resistance when turned manually.. Probably pick the lowest bidder when selecting fans for their cards