Turns out that the problem with the site was an attempted exploit by a malware bot. It failed to gain access to the site, but did manage to dork up some settings before I caught it. The site is now fully updated and protected against such an attack.
The earlier problems should be resolved; however, you may notice some increased security requirements on some parts of the site only accessible by registered users.
If you continue to have problems with the site, please let me know.