Tada! Now all of the logs in Pidgin are stored in a synchronized local folder, and you can access them from either computer. Each time you quit Pidgin it will sync the log files you create in each session between computers. As in the image below, I can now pull up the chatlogs for #instructables from July 2009, over a year before that computer was even built.
Now that you've gotten the logs synced up, head on over to #instructables!
It's been rather slow recently.
Note: You may want to disable the "Show System Tray Notifications" option to keep it from popping up all the time.
I realize that there are instructions to do this online, but I found them a bit confusing for a n00b like myself. I hope someone out there finds this useful.