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Can you press and hold down the power (top) and the menu (front) buttons for a full 15 seconds, during that time the iPad should power up then shut down then power up then shut down again.
After it has shut down the second time can you then wait a few seconds then press the power button for 2 seconds to see if it will power up cleanly and then work correctly.
If not can you connect your iPad to your computer and allow iTunes to open then select the device from the left hand side menu and you should then see the option on the right hand side to restore your device, If you can select that and then iTunes will reload the latest software onto your device and automatically restart it and then sync your library back to it so that if there was any corruption in the software it will then be fixed.
Let me know if neither of those work.