There are 4 tiny wires total. One from each side goes to the +voltage where the red wire is soldered. The other two go to the left and right marked on the circuit board. Carefully trace each one to find which one is broken and figure out where it is supposed to attach.
If you're lucky, it will have broken near the solder point on the PCB and will have enough slack that you can solder the existing wire back in place. If so, you'll want to strip a little bit (about half a millimeter) of the enamel off the tiny wire near the tip so that it can get a good connection. I usually hold the wire in one hand between my index finger and thumb with the wire tip pressed against my thumbnail, then use a knife or razor blade to VERY gently scrape away the enamel on that side. The wire underneath will be a little shinier when the enamel is gone. Do it on front and back and that's usually good enough. The main thing is to not pull on the wire while you're holding it and treat the wire as if it were a tiny hair. Perhaps "scrape" is too strong a word; try "brush" the wire with the razor. Solder the tip of the wire to the spot where it belongs. Just melt the existing dot of solder and stick the exposed wire tip into it.
If the wire has broken in the middle where it won't reach back, you'll have to try to splice it or replace it. Radio Shack sells enamel-coated magnet wire in a 3-pack. Use the smallest of the three. It's going to be quite a pain
Good luck. Ausmicro.com has some pics of the wiring too if you need it.