This an interesting problem, and I assume you have already contacted an agent for help, but perhaps not yet. I am assuming that while you were trying all these help suggestions, you did shut down the phone, waited a few seconds and then restarted it yes? If you haven't you should.
One other thing is that phone could be connected to another audio device, other than the iPhone, like headphones, or Airplay speaker etc. To check, swipe to open Control Centre and tap on the Airplay icon in the Music pane. It's the triangle with 3 circles. Make sure that the iPhone icon is check marked, and not some other device.
Sometimes ringtones get corrupted as well so you might want to switch to another one to test that theory.
Since you already tried resetting Network Settings with no luck, you might want to try Reset All Settings instead, which will often successfully solve this and other problems. This will not erase your data, but will reset your personalization settings. Good luck.
