If your headphones don't work and you know its not near the jack, the fix is easy... no more than 10 minutes if you know what you're doing. Mine took a little longer since I was working on my friend's headphones at the time and they are fairly complicated. The headphones used in this instructable are cheap pieces of junk that don't work anyways but it is the same procedure that I used on my friend's.
This should work but there are no guarantees. Doing any repairs like this may void any warranty you may have. Soldering irons and other tools can be dangerous and should be used with safety in mind. I am not liable for any damage done.
Here's a fairly well-written 'ible on the wire splicing