Is your iPad actually turned off? Sometimes the display just freezes when the display is off, and you can't turn it back on.in that case, reboot the device. Hold down the power button until the Apple boot up logo appears. You can also do a hard reset when this happens, by holding down the power and Home buttons until the Apple logo shows.
Your dead iPad could be suffering from a completely drained battery. This would not even power the Low Battery icon. In this case, just plug in your iPad and charge it for at least 15 minutes before turning it on.
If everything else fails to work, you might be having a software issue on your hands. Try to restore the iPad using iTunes. Connect the iPad to your computer, then open iTunes and click on Restore. If iTunes dos not immediately detect the iPad when you connect, you might have to put it in DFU mode and try again.