When I turn my i Pad on, I get the Enter Passcode box.
However, it will not accept my passcode.
I can get the Power Off screen but again it will not swipe to allow me to turn the machine off.
Try a forced restart by pressing both the Power and Home buttons at the same time and maintain this hold until the Apple Logo appears on-screen, then release.
If your iPad continues to have problems like you describe, try connecting it to iTunes and updating there. Remember to backup first!