The .trn file should go to a new folder in your main Dominions II folder. It might be C:\Shrapnel Games\Dominions II, but can be something else. The new folder can be called anything.
However, I think I figured out something. Yesterday, I converted (or so I thought) an old, spare computer into a server. It wasn't until today that I noticed even I cannot connect to it, from behind the same modem! I had forgotten to turn the Windows Firewall off, and it didn't show up anywhere...
Hopefully, the TCP/IP works again.