New 5s in Permanent Connect to iTunes Mode

I'm trying to activate my wife's brand new iPhone 5s. I go through the process and get to the connect to iTunes screen. I tell it to restore from her backup. It does. And after a very long time, the initialization routine starts again. I never make it past Connect(ed) to iTunes. I can see (via iTunes) that there is music on there. But, the phone itself never activates. I never get to a screen where I can do anything on the phone. I have tried resetting it to factory settings (using the restore iphone option in iTunes). Same deal with a longer wait.

Suggestions?