I have had several portable rechargeable bug zappers fail on me. I found for the most part, the problem is with the rechargeable batteries. Eventually the batteries stop accepting a charge and the zapper’s LED turns on faintly and fades away. No spark. Then finally, no LED.
I have replaced the batteries with AA rechargeable batteries, and the zappers have started working again. This time I decided to reuse an old cell phone battery that was laying around, waiting to go to the dump. Make sure to use a working battery. The one I used was for a Qualcomm cell phone. It is rated at 3.6 volts. I know this is more than the zapper needs. The rechargeable batteries that the zapper comes with, put out a total of 2.4 volts.
I had a couple of these cell phone batteries and fixed one zapper, which has been working fine now for the past month. I decided to do this instructable while repairing the other zapper the same way.

Tols required:
Phillips screwdriver
Soldering iron
Solder
Wire stripper or Utility knife

Materials required:
Old Cell phone battery
Two 10 inch (approx) lengths of wire, preferably different colours. My wire is taken from an old computer.
Electrical tape

Step 1:

Remove the screws that you see on one side of the zapper. There are 2 on the handle and 3 near the mesh area.

Step 2:

Remove the old batteries. Desolder the connections from the board. If you are going to use AA rechargeables, then leave the wires soldered to the board and just desolder from the battery pack. Please note where the red and black wires connect on the board. These are the positive and negative leads respectively.

Step 3:

Solder the wires to the battery. I use the outer contacts as you can see in the pictures. I am using the green wire as my positive. I think the inner contacts are used by the phone to get feedback about the state of the battery, so we don't need to concern ourselves with those.

Step 4:

Solder the wires to the board at the correct locations.

Step 5:

Using the soldering iron, melt a small bit of the edge of the handle, in order to make a gap through which the wire can be routed. This needs to be done when using a cell phone battery, as it does not fit inside the handle. If you are using AA batteries, no need for this. Please note that you should avoid breathing the fumes from the melting plastic. Do this in a well ventilated area.
Route the wire through the melted gap.