I am having same problem... Still
I got an iPad 2 for Christmas and have been trying to use FaceTime and iMessage on it and am having the same problem. Every time I try to sign in using either FaceTime or iMessage the page sweeps right to the "Verify" screen and then sweeps back to the "Sign In" page. I have tried multiple WiFi networks and multiple username and passwords. I have also tried closing the app out (when you double click on home page) and have rebooted my iPad several times. Both of my sisters got the same iPad for Christmas and their FaceTime and iMessage work properly. I am wondering what to do besides take it to the apple store. I heard that it might help to restore the iPad but I do not want to lose any of my stuff. PLEASE HELP!