Are you able to power the unit off? If so, plug it in, turn it off and leave it sit overnight. At least 8 hours. Sometimes they come back from weird errors like after a timeout and a good charge.
If that doesn't work (don't be surprised if it doesn't), then its time for a restore. Plug the iPad into your computer, hold down the power button for 5 seconds. Then press and hold the home button for 15 seconds while still holding power. Then the "connect to iTunes" should appear. In iTunes, select restore, and let the device wipe and install.
If that doesn't work, please update. Its possible that it could be hardware but I'd bet on a software glitch.