Following the link on the main front page, once it launches IRC, IRC continues to repeatedly try to connect to irc.darkmyst.org, with the error: "Unable to connect to server (Connection refused)".
Unable to connect to IRC
If you want, This is an alterative. Otherwise, I'm not the person who'll be able to help you. However, I'd advise you double check your settlings, and mark up here what port you're using to connect. However, the link above will let you chat anyway.
This is what I found with a quick google search: http://trout.snt.utwente.nl/ubbthreads/ubbthreads.php?ubb=showflat&Number=19391&page=1
Have you got a firewall or a router? Routers can be a real pain in the arse if you have no idea of what they do and how you use them. If your router is blocking your connection to IRC, you need to open up the appropriate ports (6666 and 6667). If you're using a university network or something similar, they might also have blocked those ports.
This site has guides on how to do that for many of the routers out there: http://www.portforward.com/english/routers/port_forwarding/routerindex.htm
Darkmyst's random server function should work correctly, but you could also try to connect to a specific Darkmyst server by typing /server intermedia.sg.as.darkmyst.org in your status window if you're using mIRC (some other clients work with /connect intermedia.sg.as.darkmyst.org also).
I couldn't find a direct IP for you to try, but if someone has one for one of the Darkmyst servers it'd be great.
If everything fails, use the link Ebok gave you. Web clients are really tacky, but better than nothing I suppose. This isn't anything anyone of us can fix, the problem is on your end.