You say the internet on the system works, but your evidence is that you can connect to your shared file server. This isn't the same as the internet, as your shared file server is most likely on your local network. Assuming you have no other network services running (like IPX/SPX, or Netware), and it's truly connecting to the shared file server via TCP/IP, that implies that TCP/IP is working on the computer. You should check to see if you can actually connect to the outside world. If not, this indicates a problem within your network, like perhaps a corporate firewall that's not allowing your computer access to the outside world. That would explain why you can't connect to NI for activation.
Assuming TCP/IP is working, you should still be able to use it within the local computer as well as within the local area network. Try the shipping examples "Simple Data Client" and "Simple Data Server". Open the Example Finder (Help->Find Examples), change to the Search tab, and enter "TCP/IP" in the search box. You can run these on your own computer - it will just use the loopback. You can then check on the local network by running the "Simple Data Client" on one computer and the "Simple Data Server" VI on another.