Actually, I think you've diagnosed part of the problem already. Clean up the wiring! And, yeah, clean the starter.
In general, apply Occam's Razor when troubleshooting. Yes, it's very remotely possible that the magnets in the starter have failed because a coronal mass ejection from the Sun induced a geomagnetic storm of sufficient intensity to alter marginally magnetized magnets. But it's more likely the wiring is boogered or the brushes are shot.
IMHO, people who would part out their own bikes would also sell their own children. (Only partially joking...)