Blackout ?

Try reset iPad

Hold down the Sleep/Wake button and the Home button at the same time for at least ten seconds, until the Apple logo appears

Note: Data will not be affected.

Run your battery down from 100% to 5% once a month to ensure accurate reporting of battery status.

Remember, heat is the biggest enemy of battery.

Might be a calibration issue with the battery, a battery failure, software problem or some other hardware failure.

Since the iPad went black and turned off the battery may be completely drained. That's not necessarily bad because this is one way you can recalibrate the software that reports how much juice is left in your battery. Use the charger that came with the iPad and plug that into a know good wall outlet. Leave it charge for at least one hour. Then, while it is still plugged in, reset the iPad. Press and hold the Home and Sleep buttons simultaneously until the Apple logo appears. Let go of the buttons and let the device restart. If the iPad restarts, leave the iPad on the charger until the battery indicates 100%.

The reset should also solve any other software problem that is causing the problem.

If the iPad still does not start try using a different charger and cable. If still no luck then it's time to have a technician look at the iPad. Make an appointment at an Apple Store to have your device examined by a technician. Or contact Apple Support.