The Home Button didn't work - single OR double-click. My usual trick of bringing up the task switcher and closing the mis-behaving app was just not possible. Even turning off and back on seemed to leave it in a knot.
What do you do when your iPad just won't respond!?
Sometimes, you need to do what in called a 'force re-boot'.
Just hold down the Sleep and Home buttons together for about 10 seconds, until the screen goes black and you see the white Apple symbol pop up - then let go of both. It may take a minute or so, but your device will then come back to the lock screen. You should then be able to unlock it, and all should then be well in your iPad world! Same applies for iPhones and iPod Touches
So far, this has always resolved my mis-behaving iPad problems!