Is ur iPad charged. Sometimes completely drained iPad doesnt even show the charging indicator.
TRy keeping ur iPad connected to charger for 2-3 hrs atleast.
After that try the reboot method explained above.
if it still fails, it maybe a display issue which may get fixed if you do a recovery (if at all its a software issue).
IN that case try doing a recovery of the firmware as per below url.
NOTE THAT THIS WILL ERASE EVERYTHING ON IPAD So DO AT THAT RISK.
If you do not have backup then take it to Apple care. They may figure out a way to take backup and check.
Recovery Ipad :
If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support