If you don't see the headphones as a separate item listed in "Control Panel" and then "Sound", on the "Playback" tab, then the system may well not see them, which could be an issue with the port.
You can try, while the headphones are plugged in, to right click on the "Speaker" (in the area mentioned above) and then click "Disable". See if the sound then plays in the headphones only. If not, or it just turns all sound off, then there is no way to separate them while using that port.
You would then either have to have the port replaced (which may not resolve it anyway) or get a 3.5mm to USB adapter and connect through that.