This isn't intended to be a question about networking. Instead, I need to understand how WP works to help debug my problem.
I host my own web server and for security purposes, I deliberately serve pages through a port OTHER than 80. That is, if someone types my web address into their browser (http://www.foo.com), it automatically gets translated into a different port number (http://www.foo.com:1234) before it hits my router. I'll spare you the details of how this is done with DNS, but it's been very effective in avoiding amateur hackers.
While this has worked for almost everything on my website, I find that WP doesn't work with this scheme. Instead, I can access the blog, but none of the CSS. When I access the blog inside the network (using a hosts entry), the blog and CSS are served correctly.
Any insight into the interaction with the CSS that would explain what I'm seeing? My next (ugly) step is to start tracing through access logs on the server, though that may not explain much. Ugh.