iPad - Restore Icon
Your iPad displays the text "Use iTunes to restore" on startup
It isn't often that Apple gives specific directions about how to fix your problem! Restoring the iPad will erase everything on it, so make sure everything on the iPad is stored elsewhere prior to restoring. To restore, connect your iPad to a computer with the latest version of iTunes installed. When your iPad appears under the devices menu, click the restore option under the summary tab. If you haven't backed up your data already, choose the back up option from the pop up window. Click the restore button to restore your Touch to factory spec.
Bad logic board
If attempting to restore the iPad and diagnosing does not fix the problem, the issue is probably the logic board.