Try this: Hold down the Home button and the on/off switch at the same time for about 45 seconds, or till the iPad comes on, whichever comes first.
My iPad 1 seemed to go dead like yours once about 1.5 years ago and hasn't had a prob since. It was working fine, was well charged, but the screen went black and the iPad seemed totally unresponsive. I did the above step and it restarted and functioned again as if nothing had happened. Hope your experience is similar.