Well, I figured out why port 7777 didn't work. For whatever reason, the install is using the IP of one of my UT99 installs, even though I installed UT2k4 connecting to the new IP and creating a new user account. The new IP for the UT2k4 server is even listed in the ./ut2k4server file. But, in the UT2k4 master server list, it's showing the UT99 IP address.
My head hurts. Time for a nap.