Hi
I make a little guess on the info you provided and take it from the start just in case.
When you run a linux server you need 2 networkcard to do what you try to do I think.
You need eth0 for your local network and eth1 for your internet connection or the other way around if you like. But I assume you got that since you downloaded moodle and got a working internet connection. You can then try typing in a browser on the server, http://localhost/moodle or http://127.0.0.1/moodle and that should work to type in the configfile of moodle too i think. Do you run apache as the webserver ?
When installing the server you also gave it a name on the localnetwork, you should be able to type that also and that should work from your windows machine. http://name/moodle since you don't got a www adress its not http://www.name.com or http://name.com just http://name/moodle .
You can browse your network in windows and look at entire network and you can see the name of your linux server there as long as they are on the same subnet. But you don't need a www adress to get to your server. You are correct in that you can just type the IP adress but the webserver need to be setup to answer on that ip adress. But to know if you configured the webserver correct we need to know what webserver. But localhost usually works to type, Also try the post above because if you see the php code it sounds like you haven't installed php.