The balance is on the right setting and it works on other devices. Other headphones do the same thing. In the past I have had to twist the thing in the jack for it to work on both sides. I think it is something to do with the jack but I wouldn't know how to fix it.
Sounds like you need to replace the jack. If it's the front port not too hard aside from finding a replacement, the rear port you are looking at a motherboard swap or a new sound card. Or maybe map one of the other ports to be the headphone out, many motherboards allow you to change the ports around.