Speaking with the voice of many years of working on electronic gadgets, it is my experience that when you are dealing with corroded battery contacts, no amount of cleaning will help. Because where you see a corroded contact, you can just about bet the wire that is soldered to it has corroded completely off, or is hanging by nothing but the corrosion itself. Kind of the old saying that "rust is what's holding the whole automobile together".
As for the old "reforming the capacitor" story we've all heard, I have learned to take that seriously enough, but only to a point. Yes, capacitors "form". All capacitors "form". Capacitors in radios, televisions, tape recorders, whatever. But in the strictest sense, and electrolytic capacitor is prone to dry out and lose its capacity, short out, or open. As far as "forming" them, I can "form" a worn-out chainsaw engine just by using more oil in the gas, and running the thing regularly. But we all know it really needs at least a honing and re-ringing, if not a new cylinder and piston.
So as for the "reforming the capacitor" jazz, take that with at least a grain of salt.