I finally got it fixed, but I ended up having to bend the pins across the top of the battery, so as to make proper contact. Since I put in a new battery, hopefully it won't need replacing during the remaining lifetime of the motherboard. I wish the socket had been like the one in my other rig, because it just has a little spring clip to release the battery. That is what I thought this was at first, and is why I ended up bending them to remove the battery.
I still find it odd that SpeedFan could read the vbat, yet the battery wasn't actually usable.