Kudos to Apple Genus Bar in Costa Mesa CA and a magic machine.

I've been around computers for a while, so when the screen my out-of-warranty iPad 2 began displaying wildly distorted graphics, I suspected the graphics card might be the problem. Instead of trashing the iPad, I restored it to the original factory settings. The problem remained. So I made an appointment at the Genus Bar, not really expecting anything good to come from it. A genus named Eli guessed that the graphics card had become unseated. He explained that the my iPad could not be opened but offered a "Hail Mary" solution. He said that the store had a machine that pushes on various parts of the case and with a lot of luck it might reseat the graphics card. I am delighted to say that it worked! And I was not charged a penny for the service. Thank you Apple. Thank You Eli.