After several hours of brainstorming we finally have a Multiplayer server running on this machine - 24 hours a day!
The ingame browser won't work due to the shutdown of GameSpy last year, but connecting is very easy. Just follow the instructions here.
Since the official documentation doesn't cover running a dedicated server at all, you will also find instructions on how to start up your own there (including the various undocumented command line switches you can use).
The server is running on a Linux box with Debian 7, via Wine 1.7.42 - renting a Windows server would be way too expensive.
Now I need some sleep - setting up DirectPlay on a Linux machine is the equivalent of hell. Have fun! :-)
(BTW, the logo is from Toan76)