It appears that the iPad may have suffered hardware damage from the drop and ensuing bang against the door knob. If that's what happened, there is not much that you can do to try and fix it.
You could try a forced restart...To force restart your device, press and hold both the Sleep/Wake and Home buttons for at least ten seconds, until you see the Apple logo.
If that doesn't help, you could try restoring the iPad.
Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support
If neither of those helps, backup your iPad if you can, take the device to an Apple Store and let them evaluate it. You should be prepared for the worst in that it might not be fixable.