Yes, the gpu is inside the same chip as the cpu. It's highly unlikely it would break by itself. I would back up everything over ssh, try to reflash, than look for a spare ribbon or lcd or both.
Most likely the screen cable. £20 on ebay. edit: To qualify that -the screen cable bends each time you slide the two halves of your computer... its a moving part - the only moving part really. And it work hardens and dies after a while. Doesnt have to be abused... just used.