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
Step 1: What You'll Need
-Wire Stripper (or similar device...knife, nail clippers etc.)
-Soldering iron and solder
-Shrink tubing (Finally found some in my house)
-Sandpaper (grit doesnt matter too much, probably something higher than ~140 should be good)
Step 2: Strip the wire
If the wire is a double, you need to pull them apart. You should pull at least 1/4" to 1/2", depending on how much you trust your soldering skills. Use a wire stripper (exact-o knife or fingernail clippers will work--be carefuler with these though) and strip the insulated wires. Separate all wires by colors (On these the colors are red, green, and copper. Generally, the colored wires transmit sound, and the (apparantly) uninsulated wire is the ground.
Step 3: Slip on Shrink Tubing
or whatever its called
Just slide it on before you twist any wires together.
Step 4: Sand the wires down.
The colors on the wires are really a thin insulating coating that needs to be removed before soldering. To do this, simply use some sandpaper and sand away until you see the copper wire. Do this with all wires, including the ground.
btw my camera really doesn't like the close-ups
Step 5: Twist and Solder
Twist all like wires together. I like to keep the grounds separate, but that is just personal preference. Once they are twisted together, put a thin coat of solder on the wire.