Phone doesn't ring, only vibrates

is the vibrate switch turned on? may seem stupid but people have done it before..

Do you have the ring/silent switch on the left side of phone set to silent (red line showing)?

I wrestled with my phone for the last 24 hours, doing repeated tests with multiple restores, to try and correct this problem. What I believe it ended up being was a custom ringtone that I had imported into my phone that apparently was not working. Therefore when the phone tried to ring, it only vibrated and gave no sound whatsoever. Changing the ringtone for the callers that weren't ringing fixed the problem. I lost almost 20 hours of time before I figured it out. Very frustrating for such a simple fix. So, check your contact ringtones and change to another for a possible fix. Maybe this will help someone else.