Ipad keeps turning on and off, flashing apple logo and home screen.

I baby the crap out of my Ipad. Used it the night before and woke up to it turning on and off. Flashing between a black screen, apple logo and my home screen (like a cycle over and over). Can't turn it off, Can't hard reset. Can't restore with Itunes because you can't turn off the find my phone in the settings. Can't do a previous back up, cause again I can't turn off the find my phone feature. It has the lastest update 7.0.6. Besides smashing it to a million pieces, what can I do? I'am trying to let the battery run out and see if it helps. But I could really use someones in put.