Even if I get it working, the corrosion on the pins concerns me. Would it keep eating away at the pins until the chip fell off or didn't make electrical connection?
That "Corrosion" is the battery acid itself and not the logic board. Logic boards use copper so corrosion there would be green or blue green in color, not red. You should be able to remove the battery acid and then then check for chewed up lines/traces. And of course - wash it (again!) to remove cap goo with ammonia, acetone, alcohol, so on. You know the routine.Continuity is the only way. Given the level of corrosion, thats a lot of checking! But really first things first. At this point is pretty much re-cap ready. I would start there, the caps. And go from there. IF you are lucky, the vias were all soldered shut. From what I see, the vast majority were. But I see a few holes, those are the ones that would concern me the most.