Try a device reset:
Device Reset (won't affect settings/data/music/apps/etc)
1. Press and hold (& continue to hold) BOTH the Sleep/Wake button & the Home button.
2. Continue to hold BOTH (ignoring any other messages that may show) until you see the Apple logo on the screen.
3. Release BOTH buttons when you see the Apple logo and allow the device to boot normally.
Frozen or unresponsive iPad
Resolve these most common issues:
• Display remains black or blank
• Touch screen not responding
• Application unexpectedly closes or freezes
iPad Frozen, not responding, how to fix
iPad Frozen? How to Force Quit an App, Reset or Restart Your iPad
Black or Blank Screen on iPad or iPhone
What to Do When Your iPad Won't Turn On
iOS: Not responding or does not turn on
Home button not working or unresponsive, fix
Fixing an iPad Home Button
iPad: Basic troubleshooting