I don't think that the solder pads under the board are related to the power switch.
To restore the two solder pads of the power switch you need to apply flux to the two circuits then just a small drop of solder at the end of each circuit. Flux will clean the area where you want to restore the solder pads and using it gives a better chance to obtain solder pads that will stay on board and make a good connection. When your solder pads are restored just solder your two power switch cables to them. Good luck...