I just fixed a magnetic valve keyboard that had a gap in a trace. From that board, I learned a few lessons:
- try to isolate the scope of your repair to just what is broken. In my case I had a dead row, and, there is a single trace that goes all the way across the board to detect rows.
- a multimeter in continuity mode (goes "beep" when you touch the leads together) is your friend. That same multimeter in resistor mode (say 0-20 ohms) can tell you when a trace is weak. This can explain some glitchy key switch behavior.
- you can (carefully!) scratch away some solder mask to detect continuity along a trace. This lets you hone in on where a trace is broken and where a repair is needed. When you are done, you can paint over with clear nail polish to prevent the trace from corroding. The nail polish comes right off with acetone. Test this on an unused part of the board first to see if acetone damages the solder mask. It should not but it might.
When you do find a gap, sometimes you can just bridge it with a solder blob. I used solder and a tiny piece of wire. I really wish I had some flux for this but it seems to be holding up.
Here are some photos of the successful repair that I did. It is still a work on progress. (Turns out I'm fresh out of clear nail polish.)
@berserkfan: Don't give up even when the odds look overwhelming.