How do I fix an unresponsive iPad screen that doesn't respond to force quit?

If your iPad is not operating as expected, try a forced-restart - as this will often clear an isolated software issue:

Force restart iPad (models with Face ID or with Touch ID in the top button)

If your iPad doesn’t have the Home button, do the following:

1. Press and quickly release the volume button nearest to the top button.
2. Press and quickly release the volume button farthest from the top button.
3. Press and hold the top button.
4. When the Apple logo appears, release the top button.

See this article. It sounds like your iPad requires service.

If the screen isn't working on your iPhone or iPad - Apple Support