First, try a system reset. It cures many ills and it's quick, easy and harmless...
Hold down the on/off switch and the Home button simultaneously until the screen blacks out or you see the Apple logo. Ignore the "Slide to power off" text if it appears. You will not lose any apps, data, music, movies, settings, etc.
If the Reset doesn't work, try a Restore. Note that it's nowhere near as quick as a Reset. Connect via cable to the computer that you use for sync. From iTunes, select the iPad/iPod and then select the Summary tab. Follow directions for Restore and be sure to say "yes" to the backup. You will be warned that all data (apps, music, movies, etc.) will be erased but, as the Restore finishes, you will be asked if you wish the contents of the backup to be copied to the iPad/iPod. Again, say "yes."
Finally, if the Restore doesn't work, let the battery drain completely. Then recharge for at least an hour and Restore again.
Well, I really don't want to recommend the next step because it's a real PIA after the fact. However...
Restore as new with NO reload from backup!
IF you choose to try it, here are some cautions. Make absolutely certain that all purchased data, such as apps, music, movies, etc., are present in the iTunes library. Also make absolutely certain that all non-purchased data, such as photos, pdf files, Word files, etc., are present and accessible somewhere on the computer's hard drive. Be aware that you will lose all game data (scores, etc.). Be forewarned that it is tedious recreating all your folders and putting each app where you want it. Finally, be aware that all passwords will be wiped out and all settings will have returned to their default values.
If the iPad is still under warranty, you're much better off contacting Apple.