Redwood posted this solution to a problem many people (myself included) are having when they try to play the new Quake III Demo Test online over at Stomped. Here's the scoop:

Some people are having problems getting the DNS to resolve for authorize.quake3arena.com. The IP address is 192.246.40.56 as stated in the readme. If you can ping 192.246.40.56 but can't get the IP from the DNS name, you can try this method that has successfully worked for some people. In your windows directory, there is a file called hosts.sam. Make a copy and rename it to hosts without the extension. Edit it and go by the sample to create an entry for the authorization server. Then you should be able to ping with the DNS name and thus play Q3 on the net. I knew that MS TCP/IP course I took years ago would come in handy one day. :) Let me know if you have this problem and that helps by posting in the comments.

Important Note: If id changes the IP address of authorize.quake3arena.com, you will have to either remove the entry from the hosts file and hope DNS is now working for you or find out the new IP address and change it to that.