This seems to be the known gpu problem with AMD Radeon 6770 chip. They lose the soldering connection because of the heat the gpu produces, the solder nearly melts and when cooling down it gets hard again and this torture brings the solder to break at any point. There has been a big replacement program by apple this ended 31.12.206 I think. The only chance of reactivating is disabling the Radeon. There is a software hack for this. But it would be better to go further and do the hardware modification too, because with an nvram reset or some os update the software hack is away and you have to do all the steps again. Google for Tiresias GPUkiller, that seems to be a stable solution.
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