As mentioned, it's probably a DSL modem. As such, the modem may also be a router. Some routers can also block IRC traffic until you change the settings. You can check
http://www.portforward.com/ for the brand and name of your router and try setting it up for mIRC there. Normally that site doesn't explain actually *connecting* to a network, but you can at least see how to get into the settings from that site and then look around for something dealing with IRC.
