For future reference for people with this issues, you can try the following:
1) Jumper the pins at the connector with the matrix disconnected to determine if it is the game board or the matrix. (OP has done this step)
2) Assuming it is the matrix, first try plugging and unplugging the connector a couple times. Be careful as the blue connectors can be damaged if too rough. This will help clean off any corrosion on the connectors. An eraser on the pins could help too.
3) Next, try cleaning the matrix itself. I believe rubbing alcohol is recommended, but so a search for that. wiring it off with a damp cloth can help. This requires the dart head be disassembled, so make sure you follow the steps in the manual to re-install it.
4) If those fail, it may be that the matrix is bad and should be replaced.
4A) if it is a single ribbon 19 pin matrix, just order a new one and reinstall. They are ~ $120-$140 from Suzo-happ or other online retailers.
4B) If you have a 3 ribbon matrix, those are not produced anymore so you either need to find a used one or update it. If you can locate a 19 pin target interface board, you can replace it with a newer matrix, but you will also need the yellow spider and segments, rubber cushion, and possibly to convert your board to use it, or find a new board with version 3.0+ on it (2.7 and under were for the 3 ribbon matrix. )