I also have Vista 64 bit, and I can use WMP to listen to BBC radio shows, (UK). I am listening to the BBC's Radio 2 as I type this.
There could be many reasons, just a few below;
1] Firewall. Is your firewall blocking WMP's access to the internet?
2] Web site. Which web site are you attempting to listen to radio stations from? Perhaps they need you to install special plugins?
3] Browser security settings. Are they set too high?
With WMP 11, I am unable to receive any radio broadcasts on my 64-bit Windows Vista pc. Does being a 64-bit instead of a 32-bit system have anything to do with the problem?