Well, took it in today. The "genius" took a look at it. They said that it was something wrong internally, probably just with the screen, but they weren't sure; they would have to open it entirely. They offered to replace it for $300. My mom asked for a manager. She came out and my mom explained the issue. Then we told them that we had twice brought in the iPad for overheating when it was still under the warranty. They went back and looked up the appointments in their system using the serial number. As it turns out, they never put in any notes based on the appointment or why we brought it in. So the manager said that someone on their end had dropped the ball. She called her supervisor and ended up authorizing a new iPad (still 3rd generation, but fresh out of the box) to be issued at no cost to us. So...don't know exactly what the issue was, but they made it right.