Have you tried completely uninstalling Avast? It's something I keep seeing in the context of people who are running into the can't connect to dbserver error, so it might be worth a try if possible.
You can always reinstall it afterwards once we know if that's the cause or not.
Gave it a shot! No dice, though. To recap, I did the following:
Uninstalled Avast.
Cleaned the registry with CCleaner.
Rebooted machine.
Ran Tequila.
Used Tequila to start Paragon Chat.
Used PC to boot COH, first without -localhost: dbserver error at the server select screen (127.0.0.2).
Closed everything.
Tequila --> Paragon Chat --> COH, this time with -localhost enabled.
Went from 127.0.0.1 to character creator.
Created character, got as far as "finish character creator and enter game" screen: mapserver error.
Installed AVG, just to see if I like it better. And here we are.
For the record, and perhaps this is important, I never get a picture in my little Paragon Chat window, just a gray field and, below that, the login stuff. No clue if that's related, but that is also a thing that is happening.
Thanks for your attention! I remain hopeful.