Hi Khaozzer,
1. Is the headphone working fine on another computer?
2. Did you try connecting another headphone and check if issue persists?
You may face this issue if headphone plugin jack is not connected to the Surface properly. You can try setting the headphone as default audio device and check if it helps:
Refer to section “Set the default audio device” from this link:
http://www.microsoft.com/surface/en-us/support/hardware-and-drivers/sound-volume-and-speakers#Add
There are set of troubleshooting steps suggested in the following link, please go through them and let us know the status of the issue.
Troubleshoot Surface sound and audio accessories
http://www.microsoft.com/surface/en-us/support/hardware-and-drivers/troubleshoot-surface-audio
System Restore disclaimer: System Restore doesn’t change your personal files, but it might remove recently installed apps and drivers. System Restore is not available for Windows RT.
Note: Perform refresh as a last option.
Refresh PC disclaimer:
The apps that came with your PC or you installed from Windows Store will be reinstalled, but any apps you installed from other websites and DVDs will be removed. You'll find a list of the removed apps on your desktop after
refreshing your PC.
Do not select remove everything and reinstall Windows. If you select it, all of your personal files will be deleted and your settings will be reset. Any apps the came with your PC will be reinstalled, but all other apps
will be removed.
Hope this helps. If you need further assistance with Windows, let us know and will be glad to help.