Well, this certainly sounds like an odd problem.
Try the old "tried and true" trick for attempting to make the iPad behave: restart or reset. Here's how:
Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears.
Reset: Hold both the power and home buttons until the screen goes dark and the Apple logo then appears (the slide to unlock screen may or may not appear). Once the logo appears, release the buttons. After a time, your homescreen will appear. Please note that it may take some time for the Apple logo to appear or for your homescreen to appear (or both). This is normal. Eventually, the homescreen will appear.
If that doesn't help, I'm afraid you might have a hardware problem. In that case, it may be time to take the iPad to the Apple store and let the Geniuses have a go at it.
Good luck and do let us know how you get on.
And - welcome to the forum!
Marilyn