Stuck in a login loop

[ Moderator note: moved to Fixing WordPress. ]

After installing WordPress on my server I seem to be stuck in a login loop. After running the installation, I’m presented with a WP login screen. I enter my user name and password, and am presented with the login screen again. No error message is displayed.

I’ve dumped my database, deleted all my files and reinstalled fresh at least three times. Same problem every time.

You can see the site at vahumanities.org

Any suggestions about what could be going on here?