From what I gather, this is self assembled custom or a switch swap.
Any more information about the board and pics of the other side of the board will help.
I most likely found one of the pins, check the pic below.
You will need to solder a small wire from the pin of the switch to the side of the diode (that little black rectangular thing).
DO NOT TRY THIS BEFORE YOU GET A DECENT SOLDERING IRON. You will destroy the diode.
Buy a cheap 30-50W iron with a small tip (not a gun, an iron.). Find an old useless PCB and start soldering and desoldering random wires on the components for practice. Don't let the joint heat up to much. If you see the flux (the yellow gooey stuff) turn black like it did on the pics, you are heating the joint too much.
The PCB is already quite damaged but it can be saved (probably). Don't rush it, take your time, practice your skills and we are here to help!