Hi there
when Firewall is enabled Doom III wont go past the loading screen…when changed to disabled or exit firewall no problems. 
:-[
J5
Most likely CPF has stopped the games attempt to communicate, and it’s popup to ask for you approval is stuck behind the full screen game you’re running.
Have you tried to Alt-Tab or Ctrl-Esc to break out of full screen mode?
Another option is to try add the application rule(s) proactively before launching the game, eliminating the popup(s) from even occuring.