Here’s how I resolved the problem (after everything I found on the internet was unable to fix it):
My wp-config.php wasn’t writable by the web server. I had had to upload that file manually when setting up the server. Resolving this can vary, depending on your server configuration, but you’ll want to make sure that the file is owned by a group that your web server is in, and the the group has write permission (755). I would be extremely hesitant to set the permissions mode to 777, as some people are recommending with the uploads folder.
This may not be of use to anyone else trying to debug this problem, but I thought I’d put it out there since I didn’t see it anywhere else.
-josh