Do you have a name server running so when you type in yourdomain.com it can direct the request to the proper IP?

If you added that line to the windows hosts file, you should be able to connect to the WebServer through the address. Question: Do you have the webserver set to listen on that ip on port 80?

A quick way to check this on linux would be using the following command:
netstat -anp | grep :80

This should return a line like this:
tcp 0 0 0.0.0.0:80 0.0.0.0 LISTEN 25802/httpd

You can also just type the ip address in the web browser and see if it pulls up a page. If it does, I would recommend configuring bind on your linux server to be an internal nameserver as well, and use that server to resolve names for your internal network.

They're on Windows, so the commands posted won't work

errr, did you miss this part of his post?

"Hi. I am running FC4 and I am trying to set up an intranet web server."