Well, it took this noob some time but, I managed to back everything up and install 2.5 with the upgrade directions provided.
For whatever reason, I have Blog Stats 1.1.1 and 1.2 both installed in my plugins directory. It was like this before the upgrade so I don't think that's causing my stats not to work.
I reactivated my plugins and the Blog Stats portion on the dashboard shows that I've had zero visitors since the upgrade, but Stat Press shows that I have had visitors.
Can someone please tell me where I should look to fix this problem?