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It is possible that the firmware/software of your iPad has corrupted. First we can reset your iPad and see if it works or not. Press and hold down the Power button and Home button at the same time until it shows the Apple logo. When you see the Apple logo, release the buttons and let it boot.
If that didn't work, that means the firmware/software is corrupted. Now your only option is to force-restore the iPad to factory settings through iTunes application (from computer) by putting it to DFU (Device Firmware Upgrade) mode, which will erase everything from it.
But if you've backed up your iPad to iTunes on your computer or iCloud, then you can restore all your data back after restoring your iPad from iTunes/iCloud. You can also redownload all your past purchases for free using the same account.
Follow the steps below to restore your iPad by putting it to DFU Mode.
First download and install latest iTunes on your computer from here : https://www.apple.com/itunes/download/
Then connect the iPad to your computer with the USB Cable.
Open iTunes application on your computer.
On your iPad press and hold the Home button and the Power button at the same time.
After EXACTLY 8 seconds release the Power button. Continue holding the home button for 20 seconds.
Click OK or Restore
Remember, it may take a while to restore the iPad (the iOS firmware has to be downloaded, you will see the Download button at the top right corner of iTunes screen. Click it to see the time remaining)
Please let me know if that didn't work, so I will continue to help you.