OK. Firstly you can set your network card to do a dns lookup or your router. The way to check, is either going to the properties or your network card and seeign if dns is set to dynamic. Another way, is to use the command prompt as above, and type nslookup. It will come back with an IP address, which should be take of your router. This means your network card is set to look at the router settings.
If above turns out to be as I expect, then I have to ask if either you or your Dad played around with the settings within the router. Most routers have an option to set dynamic DNS or fixed DNS. Most people don't plat with this, and is normally set to dynamic, which means it will automatically get the DNS records from your ISP. If you have it set to fixed, you must make sure the primary and seconardary dns IP addresses are those provided by your ISP.
If only one pc in your house is suffering with this, then it isn't your router at fault. Either your network card has had fixed dns IP Addresses applied, or your network card is playing up. I would help tonight, but a bit busy. I should on in the evenings this week, and can help you out. However DNS problems shouldn't completely stop you playing. As long as you know the IP address of the server you want to connect to, you should still be able to game. Best bet is add the server ip and port through xfire, and connect that way. Keeps you ticking over until we catch up.