I am also having the same issues on my phone. Had the phone for about 2 months. My phone does not ring...certain apps does not have sounds anymore. Checked the settings but it is still not working...wonder how many people are having these issues.
I did check the switch and the settings. Normally, when I switch the button on the side or turn the volume it will pop up on the screen but it's not even doing that anymore. Some apps have sounds...some don't. I hope the warranty covers it.
The apple store will do everything in their power to not have to go into the back room and change any parts with their phone, believe me, I have been through it with 2 mb pro's and an iPhone and iPod touch... I would try hard reset, which probably won't work, also, check if their are any updates for your phone... But As bellamri said, it is probably a hard ware issue. Best of luck..