Replace the wire, but scrape the point with a fibre-glass pen - or a razor blade (but be very careful w/ the latter option)
Use LOTS of Flux, tin your wire, place a little solder on the end of your iron and hold the wire to the point. Place the iron on the wire for a few seconds and give it a soft tug to check everything's in place properly. Then stick the wire down, reassemble and test.
Hope that helps...
LUFCfan
