The codex instuctions at
http://codex.wordpress.org/Upgrading_WordPress#Step_8:_Upload_the_new_files
have a step missing, which we might call 8.5:
8.5: download the file wp-config-sample.php and fill in the appropriate information for your database name, location, password, etc. The info you need will be in your old wp-config.php file, which you backed up. Then save the file as wp-config.php and upload it again.
I figured this out successfully, but it's completely absent from the instructions.