Sometimes when your iPad is acting strange and powering it off does not seem to make things better then a hard reset may be necessary. This technique clears the memory that apps and the operating system run in (but not your data; it will still be safe) and gives your iPad a fresh start. To perform a hard reset:

Hold down the home and on/off buttons at the same time.
Continue holding the buttons even after the slider appears on the screen. The screen will eventually go black.
When the Apple logo appears, let go of the buttons and let the iPad start up like normal.