Go to an auto parts store and get a set of detailing brushes. There are usually 3 brushes in a set, a plastic brush, a brass brush and a steel brush. Using a vinegar solution (I usually use a 50:50 solution) and the brass brush, just gently scrub the spot until all of the corrosion (the bluish green crumbly stuff) is removed.
You have done one of the most important things already. You already have a closeup picture of the spot where the corrosion is the worst. This will help in case you rub any of the traces off. It doesn't look like any of them are in danger, just the ground plane. That's the good news. When you are done scrubbing, you can go to a hobby store and get some copper leaf and solder it over the worst of the corrosion and it will be as good as new. If you scrubbed any traces off, just get some very fine wire wrap wire and solder small pieces across any gaps.
Welcome to the Arcade Board DIY club. The more of these things you do, the more confidence you will get that you CAN do it yourself.
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