Since you say you just got your computer, can we assume that it's new, and running some version of OS X? Yes, OS X comes with a firewall, but I don't recall whether it's on by default or what it blocks by default.
We need to know a lot about your setup before we can help. How are you connecting to the Internet-cable, DSL, dial-up? Who's your ISP, and where are you located (some ISPs do different things in different markets)? Do you use a router, or are you connected straight to a modem of some kind? Did you make ANY setting changes to your computer? Did you use a setup disc from your ISP-you may have received a customized browser or some sort of connection icon on the disc.
And finally, out of curiosity, what kind of Mac do you have? Are you a "switcher" (former PC user), or is this your first computer?