SilentGTX :
The extension cable has 2 plastic lines on the connector . The connector of the front panel is fully connected. The extension cable only allows the left speaker to work , no matter what device is connected to it : speakers , headphones , earbuds etc. What could be the problem ?
Try to isolate which component is causing the problem. What happens if you plug the headphones straight into the front panel? Do you get sound in both ears, and is it true stereo (i.e. you're not hearing the exact same thing in both ears)?
If the headphones work fine plugged straight in, then the cable is faulty. Getting sound in only one ear could mean one of the wires is broken. Or it could simply be that the plastic stopper on the plug isn't allowing you to insert it completely into the front panel jack. Try holding the extension plug side-by-side with the headphone plug and see if there's any difference in length between the plastic stopper to tip of the plug.
If you only get left audio with the headphones, or you get sound in both ears but it is not stereo, then the front panel is faulty. The plastic covering the jack may not be letting you insert the plugs fully. Or you have a bad connection somewhere inside the front panel or computer. The fact that you're getting a buzzing strongly suggests the front panel is at fault. Try plugging the headphones partway in.
(The other possibility was that the right headphone was faulty, but you eliminated that by testing different headphones and speakers.)
An alternative way to test it is to try the extension cable and headphones/speakers with a different sound source - another computer or MP3 player. That will help you isolate if the problem is the cable or your audio front panel.