Mark, I apologize for your inconvenience, I'm surprised that multiple hard resets haven't fixed this issue. The only thing that comes to mind is there is some sort of hardware issue, even though Airplane mode is a OS feature.
If I were you I would try taking it into a Verizon or calling Verizon (assuming that's where you purchased the phone) and seeing if you can get the device swapped out for a new one.