It nearly kills me that I can't find anyone here who will repair them when they go dead.
It's not really rocket science. Soldering is a little more difficult than using a hot glue gun, but not much. Look on the net for a tutorial. You want to heat the connection, and have the connection melt the solder, rather then the gun directly. I recommend a separate tub of flux, rather than, or in addition to rosin core solder. Flux the connection, burn of the flux with the gun, then solder as I described. Also, grub the plug with long nose pliers between the heat and the plastic, or you may melt the connector. I would cut six inches or so off of the bad end(s) of the cable, to be sure that the break/short is long gone.