Looking at those resisters, my guess is that it has already leaked a little bit.
Try adding a drop of vinegar to the area where the battery was and seeing if it reacts to anything. If it does, get to cleaning before the battery juice starts eating away at the board. It's not a fun process the stuff spreads far and wide some how.
If it's sold in your area, get the concentrated vinegar, it would cut down the wait time.
BTW, most people call battery juice, battery acid and get confused when it reacts with vinegar. Those type of batteries are basic and thus react with the acid in the vinegar.
Be Happy, it's only going to get worse.
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