Try to put your device in Device Firmware Upgrade (DFU) mode.
If you were to restore, remember to first back up your phone.
You can put your device in DFU mode (Device Firmware Update) to flush out the entire of the current firmware and reinstall it with the update file. After you got the update file,
- Charge your phone to a decent battery level
- Connect your phone to a USB port that's fully functional, not one that detects then undetects your device constantly as that's likely to brick your iPhone while it updates
- Hold Power and Home buttons for 10-11 seconds
- After the 10th second or so, let go of the home button, keep holding home for another 10 seconds (Your screen should be black or having an itunes logo)
- iTunes should tell you an iPhone is connected and put in DFU mode, please restore it
- Restore it, it will take much longer than a normal reset and restore because it uploads and rewrites the firmware.
- After everything's done, test it out again.
Note: if your Music files don't play after the restore, simply uncheck sync music and sync music, after all's done, check and sync it again.
Here's some reference