Congrats! That's one step forward! If you are inside the private network and accessing then great. However, since a Moodle is almost useless unless other folks can access, there is the firewall issue with which you might need to focus attention.
I, right now, should be able to go to the URL and see something. I cannot, however.
An nmap scan for port 80 of the diabetes Moodle server shows:
Host is up.
PORT STATE SERVICE
80/tcp filtered http
The word 'filtered' there indicates restriction to 'see it'. Now your challenge is to talk to IT again and verify that the network firewall is allowing port 80 traffic from the internet to the Moodle server.
To see yourself, you have to take your laptop OUTSIDE the entities private network and try to access your server by it's name and using a browser. Right now, no one from Texas can see your server! :|
'spirit of sharing', Ken