It appears that the problem IS RELATED TO IOS6! I am flabbergasted by the advice that I have seen from some of these high level rated users, who despite their rating don't really know what they are talking about. This isn't necessarily direct at you jobsfan. I looked at a number of 'helpful' comments gdgmacguy provided for others and he really needs to get a life.
I HAVE SOLVED THE PROBLEM FOR MY FORMERLY DEAD IPHONE and you people were zero help.
Understand that this iPhone 4's problems began with the upgrade of iOS6. The idea that hardware failure occurring during an upgrade as merely a coincidence is the most ignorant and uninformed statement I have ever heard. Hardware CAN fail as a result of malware and BAD CODE, but to make such a statement with so little information is irresponsible. Two weeks after the download, this phone became a brick, except for DFU mode. Over the past week, I have run the restore 35-40 times, with mixed results, but always ending with the phone not booting or failing to power up after booting, then being turned off. The madness included a couple episodes of the phone acting possessed. Vibrating with a lit screen and no way to shut it off until the battery died.
I tried something suggested on the boards that was related to a less severe issue.
Once I got the phone to boot again, I went to <Settings> <Reset> And <Reset All Settings>. The phone rebooted and worked for several hours before crapping out again. It took another dozen restore attempts before the phone would actually boot again. This included downloading iOS6 fresh from
http://ipswdownload.com/. It did not solve the problem either. After getting the phone to boot again, I went back to <Settings> <Reset> And <Reset All Settings>, then I also did the <Erase All Content and Settings>. The phone has been fully functional for over 24 hours. The Diagnostics & Usage Log has about 5 dozen entries of crashes, but the phone powers off and powers on like normal and is no longer a brick.
So, what conclusions can be made? iOS 6 on my wife's new 4S worked fine for a couple days before dying, then some update she did that I do not have the details to straightened it out. The problem may not be totally the fault of the OS, but somewhere in the upgrade code routine. The firmware and software updates are failing to completely clear registers, buffers or memory. You would think Apple Tech Support or Engineering would have figured this out by now. It only took me 1 week of experimentation. If you are having problems with iOS 6, I suggest patenience, persistance and <Reset All Settings> <Erase All Content and Settings>.