You are using your Apple ID email address - correct? Turn FaceTime off, sign out of your Apple ID, restart the iPad and then try again.
If you haven't set up FaceTime yet, you can't sign out in there so go to Settings>iTunes and App Stores>Apple ID. Tap your ID and sign out. Restart the iPad.
Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Go back to FacetIme, turn it on and then try to sign in that way. You may have to go back to Settings>iTunes and App Stores>Apple ID and sign in there again as well in order to download apps and iTunes content again.
Using FaceTime http://support.apple.com/kb/ht4319
Troubleshooting FaceTime http://support.apple.com/kb/TS3367
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