When you attach the phone iTunes is not recognizing it at all? It could be that the connector pins may be bent. Try holding the phone at different angles and see if it gets recognized, even briefly. If it does it's probably the connector. It will take you about $18.00 to find out.
Rather then waste money maybe you should go into an Apple store. They can diagnose the problem for you and tell you if it's the connector or the phone. You can make an appointment with them.
One other question. Is the phone charging with no issues? That was the problem I had with my iPad I had to jiggle it to get it charging and then hooking up to the computer became more difficult until it wouldn't recognize it at all. So take a look at the connector, hopefully that's the issue.