If Matt's suggestion doesn't work then you may be forced to perform a factory data reset. You'll lose your data, movies, books, music et cetera but hopefully you'll have a working tablet again.
From off, hold volume down and the power button to boot into the bootloader. Use volume down to navigate to recovery and the power button to select recovery. Once you see the android on his back and a red exclamation press and hold the power button and press volume up once to enter recovery mode.
Now press volume down to scroll to wipe data/factory reset and press the power button to select it and then scroll down to Yes - Wipe all user data, again pressing the power button to confirm.
Your device will be reset to factory values and you'll then need to set up again.
Sent from my Nexus 5 using Tapatalk