Whatever happened in the end? Was it the GPU?
I'm having this very same issue. But with a GTX 1080.
I don't have any spare components (Psu,GPU,mb) to test out. But the PC works without GPU. (I7 6700k, Asus Ranger VIII)
So I guess it's safe to assume that I'm in the same boat as OP? And my GPU shorted internally?
I have warranty.