I have never seen anything like that. Did you try a forced restart of the iPad? It is sometimes called resetting the device. It's not like powering off and on with the power button only. If you have tried it, give it a shot.
To force restart the device, press and hold both the Sleep/Wake and Home buttons for at least 10 seconds, until you see the Apple logo.
If that doesn't work, try Settings>General>Reset>Reset all settings. No data is lost but de ice settings have to be re-entered, such as your WiFi network passwords. So if you don't know the password by heart, get it before you reset the settings.
If that fails, you could try restoring the iOS using iTunes.
Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support
If that still doesn't work, you have a hardware problem. Make an appointment at an Apple Store and ask them to evaluate the iPad for you.