To me it looks like the battery leaked enough to warrant a good clean-up of the board, but since you're newer to the solid state stuff and if the board is working fine right now then it's not *horrible* to use it as-is for a bit. At least gives you the chance to try the game & see if you like it enough to buy another board or attempt to clean it up further. The only thing is, if left as-is it will at some point kick the bucket. Personally I'm not a fan of leaving a machine on & unattended for hours on end if there are corroded boards in it that haven't been dealt with.. in case something locks on or shorts when the mpu eventually goes bad.
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