I swab the corroded contacts with white vinegar from the kitchen. It turns the white gunk into a foamy blob, and I assume it etches off enough of the corrosion to restore conductivity. I wipe the foamy part with the dry side of the cotton swab, and the device usually works again.

I started doing this as a kid, reasoning that the white gunk looked like baking soda, which is fun to combine with vinegar, so let's see what happens. I just looked it up, and it appears that the process is legitimate and safe. The vinegar turns potassium carbonate into potassium acetate, also producing carbon dioxide.