I use Norton Ineternet Security, and I don't have a problem with web radio. Moreover, my Norton settings are the most restrictive possible--I don't allow ANYTHING until I approve it--so I'm confident you can get web radio going.
One possiblity is that MC is trying to access the internet and you're not allowing it. MC must access the internet in order to recieve web radio. There are two places to check. First, open up the firewall gui.
1. Double click "personal firewall", click "custom level" (near the bottom), and make sure "Enable access control alerts" is checked. If you don't have a policy yet for MC, this is a handy way to do it as you go. Now click "OK".
2. At the top, click the "programs" tab, and go through the scroller looking for "media center". If media center is there and listed as "blocked", you need to change it to "permit all". BTW, the are 3 programs within MC that will try to use the internet. MC, "download manager", and "package installer".
NEVER disable your firewall. The people who recomend trying this are out of touch with current events. It takes less than an hour for somebody to find you, and then your IP address gets written on a bathroom wall, and everbody tries to visit.