Sounds like the ports you're using to connect to them are being blocked somehow. Are you behind a proxy?
You said it reports being able to lookup the irc address when it's trying to log you in, it could be an authentication issue. Do you have identd installed?
Please cut paste the exact transcription if you need further help isolating what aspect of the connection is that's getting bogged down to cause the hang.
Edit:
Ok, if you're at work then you're almost assuredly being blocked and the log you posted appears to back that up as spartan as it might look on the surface. Assuming you don't have access to administer your work's firewall are you aware of what their policies are? IRC would be considered a pretty gaping circumvention of security if your work is at all worried about unauthorized access or malware making its way into onto their subnet outside of detection. Some places just don't like employees being able to waste time on irc.
Logs seem to point this to this conclusion as your initial TCP handshake is confirmed but the irc server is unable to send you any further independent authenticating packets because your company's firewall is blocking traffic to 6667. If it was an identd problem it would have said so. You might be able to circumvent that by setting up port forwarding on your local machine to use non standard ports in the high 10000-65536 range. Not sure how sophisticated their traffic analysis is, so you might get in trouble without further knowledge of what their policies are, you might want to find out. There are a number of ways to disguise your traffic without detection based on what they're setting up to block you. It could just be as easy as them blocking the port, or doing traffic analysis to block signatures. If it's the latter, then port forwarding alone won't work.
