Obviously replace any frayed, worn wiring. Fuses are cheap, and easily replaced so you might as well take care of them, too.
As for using the original power supply, I'm still using my Defender power supply, and it's about 25 years old. As long as the thing is clean, and the wiring is in good shape, I'd say use it.
Doubt that the power supply is the reason your switch zapped you.