You probably already did this but I've gotta say it just to be sure: Try the number again and make sure you have typed it exatly as it is shown (i.e. capitols, dashes if you did not try that before, etc.)
If that didn't work, all I can recommend is check your e-mail and see if there is a responce to your ticket there. If there isn't, send a new one as it's likely they never recieved it. (Usually you'll get a we're looking into it message back pretty soon after it's sent.)
Could also look and see if the game is under your purchases on impulse. If so you can install it from there as well. That would have the most recently updated version of the game. (It may show up as Sins, Entrenchment, and Diplomacy there though, as Trinity is just a compilation of all 3 games, but I'm not sure as I bought them all seperate.)
If you have never used Impulse, it is the program sins uses for updates. Your login information is the same as you use to log into these forums.
If all else fails, I believe when I bought the original game the serial number wasn't required for single player, just online play. If that hasn't changed you should at least be able to familiarize yourself with everything while support gets this sorted out:
support@stardock.com
-Twilight Storm | Sorry if none of this was helpful