Very Strange IP/Domain Name Looping Issue

I am running WordPress 2.3 on an Ubuntu server 7.04 installation with LAMP (php5, apache2). WordPress is installed at the server root (/var/www). Just to be clear, the files that were in the original WordPress directory have all bee moved to /var/www.

Everything works nicely via the internal IP address. However attempts to reach my blog via https://www.mydomain.com are timing out. The same thing happens when I try to hit the blog via the external IP. I can see in the bottom left corner of my browser that the domain name and the external IP are looping continuously until the attempt fails.

This sounds like a normal DNS problem, but please read on before telling me that’s my issue.

Some important observations:

1. WordPress works fine when accessed through my local IP.
2. https://www.mydomain.com/wp-admin gets me to the admin log-in and on to the site. Works perfectly.
3. https://www.mydomain.com/egroupware gets me to my eGroupware installation also running on this box.
4. My WordPress install did not generate a .htaccess file. I have not created one.
5. If I drop an index.html file at the root (/var/www) https://www.mydomain.com it opens up just fine.
6. My apache2.conf has the server root set to /var/www.

Any help would be much appreciated.