I'm sorry I'm pretty stumped on this one, those steps would normally fix an app misbehaving. The only place I can think of an indirect setting for photo booth is through the Restrictions tab, when the camera is restricted it also restricts photo booth, but the icon will then disappear. I'm hoping someone else knows more on this issue. In the meantime I would try another reset, I once had a problem with the zoom feature and I had to reset 4 times before it stopped.
I really hope it is photo booth you are speaking of here too, as I assume it's an auto correct that you have phone booth.