Well duh. Sometimes the hardest things to see are the things in front of your own nose. Thank you gentlemen.
Thanks for the quick reply, esmi. Can you tell me what changes (in general) the host needs to make to fix this? FYI, a couple of weeks ago the site owner did actually contact the host about this problem, and was told to update the site. Host provided a link to these instructions:
http://codex.wordpress.org/Updating_WordPress.
Needless to say, nothing further happened.