The GPU, video chip, on your mother board has a compromised BGA (ball grid array) or the chip itself has died, more than likely the BGA is the problem. If the BGA is the problem it usually can be repaired by reflowing it, instead of reballing it. I would recommend attempting the reflow yourself or replacing the motherboard. There are people on eBay charging $250.00 for such work on an Apple. The ifixit has [product|IF183-042|your motherboard here.] for about $279.95 + shipping. I haven't been able to find a decent guide for you that is done specifically on your board model. If this is something you may want to attempt please let us know and we will find a guide(s) for you.