Have you tried logging on to the CC.NET box as the user under which the service is configured to run and firing up IE? You'll probably find that there is a dialog to specify initial options like Internet connection that the user in question hasn't yet OKed on that machine.
Detailed instructions:
Make a remote desktop connection to the server, or log on to it physically if you have access, using the logon details under which the CC.NET service is configured to run. If it is configured to run as the local system account, you will need to configure it to run as a user account instead to get this working.
Once on the machine, fire up Internet Explorer, and my guess is that you will be presented with the dialog for setting up your Internet connection. Go through the wizard and OK everything. Then log off again. Now, when you try to run your CC.NET build, you should find it works.
Alternative:
You should be able to disble this wizard for the local system account. Check the following registry value:
HKEY_USERS\S-1-5-18\Software\Microsoft\Internet Connection Wizard\Completed
This should have the REG_BINARY value 01 00 00 00. S-1-5-18 is the fixed SID for the Local System account.