Did you hold the buttons down long enough? Try it again and wait a little longer before you release the sleep and home buttons.
Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.
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