The Problem
My son let his ipad run down really low, and then his brother accidentally unplugged it shortly after it had been set to charge. The net result was that the screen went black, then when we plugged it back in to charge we just got the apple logo.After a few hours it was still the same. It didn't appear to be charging and refused to start.
The solution
I fixed it by putting the ipad into DFU mode and left it plugged into the charger overnight.- Hold the Power Button (3 secs)
- Continue holding the power button and also hold the home button (15 secs)
- Release the power button while continuing to hold the home button (10 secs)
The next day I forced it to shutdown by pressing Power and Home. You should then be able to start it as normal and it will show a 100% charge.
Hopefully this will work for you, good luck.