had a not the same but similar problem, just in the off chance its the same thing, try this.
Connect to the IRC server using port 7000 instead of 6667. (if this works it was likely a conflict with your routers inbuilt ability to try and handle irc dcc sends [if it has this ability at all]).
* im assuming here that, the mirc has a set range of dcc ports selected under alt-o/connect/options/advanced and those same ports are forwarded in the router to the pc in question, as you have stated. And your firewall and protection scheme issues have been clearly shown to not be the problem.
