|This sounds like it could be a DNS issue.|
Is this your wireless network in your own home on a SOHO Router you own?
If it is, and you have another computer that does browse properly you'll want to open a command prompt window on both (Start >> Run >> type cmd and hit Enter) and run the following command:
Now compare the output. The only thing that should differ is the actual IP address. Pay special attention to the DNS address, if this is different, then that's your issue. Web browsers rely on DNS to be able to connect to websites.
Chances are your itunes software has it's own server's IP addresses hard coded into the software itself and thus doesn't require DNS to resolve it.