Once you remove that battery the board could possibly look a lot better when you clean that area. Maybe there are no board traces that are eaten away, just battery crap on top surface of the board. Worth a shot. After removing the battery clean the board where the battery leakage is by using some vinegar, then a little soapy water. Can use a toothbrush to scrub (preferably not your wife's or girlfriend's). Then use fresh water for final cleaning. Let dry thoroughly and examine board with magnifying glass for damage. If there are one or two damaged board traces they can be repaired with small bus wire soldered to the board.