i am experiencing the same problem. I restored and updated my phone to the lastest ios update (6.1.3) then reset my network settings and it still did not work. I went on apple support and chatted online with a representative and they informed me that it must be a hardware issue meaning you would need a new phone. if you are under warrenty you can just make an appointment and/or mail in your old phone for a request of a new one free of charge.
If it's still under warranty forget the troubleshooting; just take it to an Apple store and get a replacement. Make an appointment first: http://concierge.apple.com/reservation/us/en/techsupport/