iPad mini screen rhythmically turns off and on every 2 seconds.

I was asked to fix an iPad mini for a friend, but I've never seen this problem before. I did a full restore in DFU mode and everything seems to work, except the screen continually flashes on and off every 2 seconds. 2 seconds on, 2 seconds off. The digitizer continues to work when the screen is black, and it isn't rebooting itself, just turning on and off. If I leave it alone for awhile, it turns itself completely off, even with lots of battery left. I'd appreciate any suggestions!