I got the chance to examine the board today. There are a few traces where the solder mask is darker than other areas with battery crud nearby. There is also one via whose solder is white looking. I figure that it would be best to redo the solder in that via. How would I remove a little bit of the solder mask to test the continuity through the suspect areas without damaging the trace?
One of the BIOS chips had some battery crud on it as well, but I removed it and sprayed it with contact cleaner and replaced it.