I've got the same issue as well on my iPhone 4S - ring tones work, but music or app sounds won't play. In the sounds menu, my volume is high, with "Change with Buttons" set to "On." However adjusting the volume buttons just says "Ringer" with no volume scale, and there's no volume bar when playing music or videos. Originally this issue was just without headphones, and then it fixed itself. But now the issue is with or without headphones, no volume bar is visible in either situation.
Alarms, message alerts and ringtones have worked throughout.
Image one - Video with headphones in (before it stopped working with or without headphones!)
Image 2 - no headphones (before both stopped working) - volume bar disappears!
Same again in the audio menu at the bottom of the homescreen:
With headphones:
No headphones (sometimes the volume slider appears, only to disappear the second you try to touch the slider!!)
Turning the iPhone off and on seems to have no luck, I'm not sure what solved it the first time, but now I can't play any music or videos with or without headphones!