Only problem I've had with my iPad was once the battery was under 10% and I wanted to run it completely out to do a full charge. I left a video running and walked away. About an hour later I went to check that the iPad should have run out of battery by now but instead the screen was frozen on the video. No matter what I did I couldn't turn off the iPad or get off that frozen video screen. The battery eventually gave out after a few hours and the iPad returned to normal after a charge.
So I've had a problem powering it off but never a problem powering it on. I would just chalk it up to random electronics behavior for now. If it happens repeatedly then you should bring your iPad to Apple for repairs.