Because I have to wiggle the cable around the USB end to get it working it was pretty evident that the problem was one or more broken wires within the USB plug. Hence the solution was to strip the plug apart, cut out the dodgy cable and re-solder the cable onto the plug.
Needless to say I wrote this instructable with a nice working mouse! Oh and this is my first instructable, so enjoy!
Step 1: Cut Off & Cut Open
Next we stand the plug on its side, with the exposed metal part up in the air. The exposed metal is the bit you want to hold onto so you don't cut your fingers. Now using a stanley knife or similar to cut one side of the plug. (See the photos!) You want to use a fair amount of pressure whilst moving downwards with the knife, just please please please be careful not to cut yourself.
You want to cut until you can part the whole rubber/plastic casing and extract the metal innards. Hopefully you shouldn't have to cut the other side of the plug.
Step 2: Get to the Wires & Prepare
Now we've done that we need to strip and prepare the wire that's going to be soldered to the plug. I would suggest the sure of a proper tool here and a lot of patience. Else this step is just going to end up with a load of broken wires. See the photos for a target.
Step 3: Tin & Solder
The fist thing to do is to tin the wires, making them much much easier to work with later. For those who aren't aware tinning is applying a thin coating of solder on the outside of the wire. Next we need to strip out the gunk currently on the connector, I used de-soldering wick here but use whatever de-soldering method your happy with.
Next we take the wires and solder them to the connector/plug. Remember which wires go where!
Once soldered this is the prefect time to test the connections, plug it into your computer. If it works all good, if not go and find out why. Your most likely reason will be because of shorts. Check the joints where we've soldered then check again. Running a flat head screwdriver in-between the joints is also a effective way to make sure there are no shorts.
Step 4: Put It All Back Together Again
Once you've got the metal part back together the last step is to put back the rubber/plastic outer mould. This is best done by placing it around the metal using, a fair amount of hot glue gun glue in-between the two sides of the cut. Then being pushed straight together. Let the glue dry then use the Stanley knife to cut off the excess (this is why I used a Hot glue gun.)
We have now repaired the USB cable, the last job to do is to put it to good use!