As a follow up to my above post. I called apple support. They were very helpful but were not able to solve the problem after we did several DFU (?) restores. They then made an appointment for me to see the Genius's at an apple store the next day. The genius there was very nice but he was also unable to solve the problem after also doing an DFU (?) restore. He then directed me down the street to the verizon store saying it must be a verizon problem. But alas, the Verizon people were unable to do anything after trying a number of things. They said since the message was to called Apple/Support it was an Apple problem and directed me back to the Apple store.
So, I went back to the Apple store and since my 8Gb Iphone 4 was still under warranty they gave me a new one that was still loaded with IOS 5.1.1. I am not going to update this one to IOS6.
I had same problem on my iPhone 4S. After many restores using a DFU (device firmware update) and iTunes or wifi activation failures, the Apple 'geniuses' had no luck either and gave me a replacement iPhone -- thang goodness it was less than one year old so stil had some warranty protection left. Very disconcerting though, I thought iPhones were more reliable than that! After all these are not inexpensive devices. I feel certain it had to do with the iOS 6 upgrade but 'genius' said could be just.a coincidence. Hmmmm... At least the replacement is per loaded with ios6, so don't have to mess with that again.