There's a lot of things that can go wrong with IRC connections. Some particularly bad ISPs (eg: some universities, apartment complexes) filter IRC traffic. Usually this is just the default port, so try an SSL port or an alternate port. Currently, GotWoot IRC listens on 6667 and 7000 for regular connections, and 6668 and 6697 for SSL connections.
Some virus scanners and personal firewalls also prevent IRC traffic.
If you're stuck, consider posting them in the General Support section of our forums.