I had the very same problem with my 4870, baked it and its been working just fine ever since. give baking a try. i take it your card is out of warranty so nothing to lose really.

Gather ye old aluminium foil for covering and a heat gun in circular motions over the chips. Oven method makes all your subsequent pizza's toxic, and there is also running the risk of having everything fall off the board, or bake to a crisp. 🙂 If it's the VRAM memory that's fried it likely wont work anyway to reflow the BGA solder but nothing to lose at this point.