If the port is on the board itself for onboard sound it would be a task for the non experienced soldier to see that replaced. Radio Shack has all the mini jacks for projects seen there. The mini jack is a two channel 1/8" mini plug type.
Sometimes the software for sound can get goofed up as well. You can try right clicking on the Sigma Tel onboard sound item found in the sound, video, and game controllers section in the device manager to select the update driver option there to see if Windows will automatically locate the latest version to see if that corrects it.
The support site for the system if prebuilt will generally have their latest version for onboard found there to reinstall a fresh set. A bad connection in the jack however is not good since the jacks are usually seen inside a preformed plastic enclosure while a substitute from Rat Shack might work if needed.
One thing needed here would be the make and model number of the sysem for the quick look for updates. But this is one reason why I always run a separate card plus the improved sound quality of an expansion card with the onboard as more of a temporary alrternative if a card goes doa.