Cut the wire back till you have about 3/8 of clean wire showing. Cut you a piece of heatshrink about 2 inches long and slide it over each wire coming from 1 side. Put some flux on the ends of each wire end and then proceed to tin them with some rosin core solder or silver solder and a soldering iron. After each end is tinned, hold each pair of wires together and heat the ends with the iron. The solder pre tinned to the wires will fuse to create a tight bond and electrical connection. Once each wire is completely soldered together, slide the heatshink down over the soldered joint. Heat the heatshrink with a heat gun, but you can use a lighter if you are very careful and take your time.

Repairing the wires this way will make a permanent electrical connection and ensure you that this isn't the problem again if this doesn't fix the issue.