How to fix the sound on my iPhone 4?

I have the iPhone 4 and when i got it i downloaded an app and the audio didn't work. I had the sound fully up and it did not work. I can't turn up the audio unless i'm in music and sound doesn't work on anything but YouTube, Skype, Camera/Photos and only texting apps, I have not used the phone on it yet so i don't know if it works or not. My setting on sound are, Vibrate on Ring off, Vibrate on Silent off, Ringer and Alerts (Full), Change with Buttons on, Sounds and Vibration Patterns (All set to something) Lock Sounds off and Keyboard Clicks on!
Please help, i really want it to work, i would get an iPhone 4S but i'm not sure if i'm able to return this iPhone 4.

Added (1). There's no mute, so mute was never on

Turn mute off.