a tooth brush and baking soda is in order for the battery chemicals.
just scrub the battery compartment with baking soda and water to
neutralize the chemicals. i think that fumes from the leaking batteries
get into the electronics and leave residue even with no direct contact.
a slight coating of conductive residue is left on circuits that causes
all manner of havoc at the micro voltages present in modern
electronics.(even cigarette smoke is bad because of this!) that would
account for the erratic way its working. maybe a quick spray out with
zero residue cleaner or similar electronic cleaner might help the actual
circuit board. leave it unpowered for several days to make sure that its
completely dry.