Sometimes, after the iPad has fully run down, you have to reset it.
So, do this: Press and hold both the sleep and the home buttons until the screen goes dark (you may or may not see the "slide to power off" screen). Just keep holding until you see the Apple logo, then you can release the buttons. Eventually, you should get the iPad homescreen.
Waiting for the Apple logo or the homescreen to appear may take a while - just hang in there and wait.
Hopefully, the iPad will respond and then begin to work as normal. Do let us know how you get on.
Marilyn