Quoted from vireland:
Hard to tell from the resolution, but it LOOKS like two pins at the right end of the chip at U42 are corroding, too. Maybe got dripped on? I'd check everything DOWN from the battery holder carefully.
All the top pins on U37 are suspect, as is the little green (capacitor?) to the right of U42. I'd say on U42 itself, it's the SIX pins on the right, with the two closest to the center probably okay, but those 4 adjacent to the right end? Definitely.
Just neutralize what you can find and clean the acid off you use to do it. This thing is far, far from a difficult fix. Unlikely to even need to unsolder anything anytime soon.
+1 on the NVRAM or remote battery holder.
*Edit* If you don't know what you're doing, don't even think about working on the board with a soldering iron. Solder that's been corroded is harder to work with, and you're more likely to pull a trace when removing components. Battery damage and corrosion is one of the few things I recommend people use a tech for, and I've never paid a tech in the 7 years I've owned games (because I chose to replace boards..all the ones I had with acid damage were massively damaged across 40%+ of the board. Yours is VERY salvageable!). If you screw something up with poor rework, most techs won't even touch it at that point, much less the few that are actually good at repairing alkaline damage.