After making some changes to global settings in Joomla, all the links broke. The site was unusable, and only now have I figured out why.

 As it turns out, certain things happen when you enable "Search Engine Friendly" links in the global configuration. I solved the problem by moving htaccess.txt to .htaccess and enabling apache mod_rewrite in the global config.

 Now I have to fix some of the linking changes I made while I was troubleshooting.