Someone could have told me you needed help with this.
Yes if you're in there all alone, you are definitely in the wrong place, I never turn off my PC and being on broadband, I leave my IRC client open and connected. The only time I’m not at least idling in there is if something unexpected happens. Even if that were the case the channel is registered so any time a user joins if the channel is at that point in time empty a service bot will also join.
As for clients, I don't recommend ChatZilla, I just find it to be a bad client, though that’s only my personal opinion. KVIrc would be your best bet, it's a visual client. This means that it doesn’t have the scripting capabilities of say something like mIRC (Though for your average user this isn’t an issue), but it’s much more aesthetically pleasing.
As far as Trillian goes, I can’t help sorry, when I tried it out long ago either MSN would work and nothing else or everything would work and not MSN, so I ditched it. I might talk to one of the service admins for the network about setting up a java applet for the site, that way you won’t have to worry about an individual client.
If you’re having problems try irc.p2p-network.net:6667 as the server address, channel is #DOSgames I will say yeah it’s not the most active place in the world, but it can be fun if people put in a little effort. As Pancake said the more people that come there the higher the chances are for chat. And if no one else is online while you’re there, you can always play trivia with DOSBot.