Try this: Hold the power button on top and the app control button in the center (The big One) and just hold it to the phone resets/restarts.
Have you tried restoring with iTunes?
You might want to make an appointment with the Genius Bar at an Apple Store and have them take a look at it.
Oh my, Beckinator! Did you try the steps that Elector suggested? That is normally a sure way to restore activity on your phone.
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I have had the same issue for past week with my iPhone 4. I had connected it to desktop to update to iOS7 from iTunes store and my phone is totally frozen with a picture of iTunes icon and picture of phone connector. I have tried EVERYTHING to restore it. Holding down power button and Home button at same time, reconnecting back to desktop PC to regain control, nothing. The Verizon store in my area closed down and I'll have to travel 1/2 hour or more to get to real Verizon location. I ordered online a brand new phone, iPhone 5c, just received today but don't want to activate it until iPhone 4 is restored so I can make sure all my photos and contacts are going to transfer over. Any other suggestions for unfreezing?