If you are unable to open your iPad and it does not recognize any home-button presses chances are that you have activated Guided Access in Settings > General > Accessibility > Guided Access (Under the LEARNING tab).

To get out of this mode you need to click the home-button three times, enter your passcode and then (in the top left corner) press end. If you don't want guided access turned on, you can disable it.

Guided access is useful if you are sharing your phone with someone else but want to restrict that user into only being able to navigate inside of the currently opened app.

Hope this helps.