Well, my buddy seems to be having the same problem. He keeps describing things excactly the same as you, Black Screens, Sleep Mode, Video Card Fan Not Spinning.
He said when he turns his on from being cooled down (sitting off for more than 10 mins or so), a small amount of display shows up, but very scrambled (pixels missing / moved / etc.).
Is there any easy way to determine whether the whole video card is shot, or rather we just need to order him a new heatsink / fan for it?