You might try removing the battery and motherboard, and cleaning it with
denatured alcohol or MEK. Won't hurt the motherboard, but it does remove
the corrosion. If the corrosion is severe, check the solder joints for
damage.
THe battery electrolyte is most likely alkaline (potassium hydroxide?) and
a chemically weak acid is quite useful or shifiting it. I use a
solution of citric acid, it smells nicer than vinegar :-)
Of course if the corrosion has damaged tracks on the PCB, you've got a
lot of work ahead of you...
-tony