This was driving me nuts. I just had imaged and installed three computers with Windows 7 64 bit, customized them with some computer-specific software, and then one of them acts up. I can access the local network resources, but I can't get to the Internet. On ONE of them.

It took me many hours over a few days, but I finally found the solution in a thread at Windows 7 Forums. Here's the part that helped:

For those of you reporting problems with your network after updating MS Office or installing Adobe CS3 -
If you are having Internet connection problems related to "Unidentified Network" showing and the "!" over your NIC icon, then this should take care of it:
Check to see if you have this little devil in your services list:
"##Id_String2.6844F930_1628_4223_B5CC_5BB94B87 9762 ##"
If you do, stop it and disable it. It is actually the Bonjour DNS Responder Service, and I believe it is the cause of the "Unidentified Network."
The Unidentified Network disappeared after stopping this service and a quick disable/enable of the NIC, restoring Internet access.