Okay, so basically here’s what happened. There was a botched install of WordPress, so there was a WP-Admin and a WP-Content directory in the /Public_HTML directory, but no WP-Includes directory. I had been working in the botched install directory, and was confused by the directories in the public HTML directory.
While I tried to update the Admin and Content directories in the public HTML directory, I hadn’t imported the WordPress files or the WP-Includes directory.
So, the advice offered here was entirely correct. Especially GRAQ’s suggestion to move the WP-Includes directory in. I was halfway there, and when I imported the WP-Includes, I was able to update the database and everything is now working smoothly.
I took what I learned, and updated another website to 3.1 afterward without a hitch.
Thank you for the assistance!
