Things to try.
Hold down the power and home button until the Apple logo appears. Ignore the power off slider if it appears. Let the device reboot.
Go into Settings > Brightness & Wallpaper, turn off Auto-Brightness and up the slider.
And if neither of these works, and I don't really expect them too, call Apple Support. Your iPad is broke. If it's under warrantee (less than a year old or has Apple Care) they should replace it for free.
You might want to connect it to iTunes, Transfer Purchases, Backup, and Sync before taking it to the Apple Store, or sending it in. It will make setting up your new one easier.