Have you tried to do a soft reset or a hard reset? To do a soft reset, all you need to do is hold the power button and the home button at the same time and hold them down for about 10 seconds until you see the apple logo. This has fixed this issue a few times in the past. If this doesn't work, I would recommend doing a hard reset. To do this, you have to go into:

Settings > General > Reset > Reset All Settings

This will reset all of the settings in the phone and should allow you to see it in iTunes. This will also delete all data from the phone. So just be aware of that as well. I hope this helps.