Have you tried pinging an internet site, something like ping yahoo.com? If that fails, try pinging your DNS and gateway. You may even want to try a tracert yahoo.com and see how far it gets, that can usually give you a good idea of where a problem may be.
Check your browser settings to be sure it isn't looking for a proxy server (or if you are using a proxy, check that it is configured correctly).
Double check your NIC configuration, making sure IP address, subnet mask, gateway, and DNS servers are correct.
Beyond those suggestions, can you give a little more detail on how your connection is set up? DSL/Cable through a router? Dial-up? etc? Has anything changed on the computer or network devices since it stopped working?
Hope this helps!