DNS problem due to website

We have a website that is setup as http://www.clientname.com. We also have a Windows 2000 Server running DNS with the same domain name of clientname.com. We’d like all the internal workstations to use this internal server as the DNS server.

However if you specify it in the network settings when trying to get to the webpage it says its not found since its looking on the local W2K server instead of the Internet. How can I change our domain name internally without a lot of time and work?