Black blocks on screen, runs slow

This is an iPad 3 AT&T. I have the AT&T connection turned off.

All of the apps work, but black blocks of varying size appear on the display, and the iPad is running slow. I have restored the iPad to factory settings, no difference. I understand this is probably a hardware issue, but the question is, what part? It's no longer in warrantly, so a trip to the Genius bar is no longer an option.