Does your firewall route incoming connections to your computer?
If you're posting this msg from the routed computer, I assume it works correctly.
You need to open a range of ports for uploading (see mIRC options > DCC > Options), but not for downloading, as it opens random ports on your computer (like web browsing, email retrieving, etc...).
By the way, no need to open TCP port 6667, it's only for servers, not clients (don't know what's the TCP 194 for).
So check if your firewall has its NAT route configured for IRC. If your fw is running Linux, iptables needs to load the IRC conntrack module.
If nothing works, read this post: http://forums.mirc.com/showflat.php?Board=connectionissues&Number=17