The attachment Asus P2B-VE test bench 2.jpg is no longer available
Did some more testing of the motherboard.
I switched to the built-in ATI Rage 3D video chip and that seems to be working fine. I tried the POST card in all the PCI slots and no abnormal results there.
I further installed an SB16 sound card and tried some games under DOS. Everything worked fine.
Between testing games and more benchmarking, I probably ran this board for 30-45 minutes. No crashes, lockups or signs of overheating issues.
I re-ran Speedsys since in the first benchmark there were some funny dips on a few of the tests. But this time the bar graphs were perfectly smooth.
The attachment Asus P2B-VE Speedsys ATI Rage.jpg is no longer available
For that one corroded via, I cleaned it out as best I could and applied some thin solder mask to protect the copper. It dried transparent so it's barely noticeable.
I don't think that via would have been an issue, since the corrosion seemed to be a surface issue as a result of the exposed copper. I am confused as to how it was exposed in the first place, since there are no other scratches or damage around it.
The attachment Asus P2B-VE exposed via.jpg is no longer available
Insofar as the symptoms the OP was reporting, I'm a bit stumped. Because the board itself is working, I'm assuming the issues were elsewhere. Since the OP reported the board stopping at a memory related POST code, maybe there was an issue with a DIMM? Even just dirty contacts? I gave the memory slots a spray with some Deoxit for good measure, but they seemed fine to me.
I wonder if the low CMOS battery might have caused some issues? Although it should have still allowed the board to boot.
As for the burning smell, since the OP mentioned a fan not spinning, possibly the fan itself burnt out? I've had that happen before and that can result in a burning odor.
Other than that, the board appears fully working and in great shape.