EDIT: I've resolved this. Nevermind :)
I'll try to give as much info as possible, and any help at all is greatly appreciated.
I have this Windows 7 machine, and I'm running a Fedora 17 VM on it using VirtualBox. Within the VM, I am hosting an apache-tomcat6 server. I need other computers on the same network as the host machine to be able to connect to this apache-tomcat6 server.
I've gotten the VM assigned a static IP. Within the VM, if I navigate to "https://129.83.174.205:8443/HisPortal", it works! The website loads. However, if I navigate to the same URL on a different computer (connected to the same network), I get "This webpage is not available."
When I turn on the VM, all I do is run "service tomcat6 start" and "service mysqld start"
If I ping 129.83.174.205 (the VM's static IP) from another computer on the network, I receive a response just fine.
Here are all the images I think could be relevant/helpful:
The network settings on virtualbox: http://imageshack.us/a/img222/690/networksettings.png
The server.xml file in tomcat: http://imageshack.us/a/img854/9895/serverxml.png
Well, this embarrassing.
All I had to do was disable the firewall on the VM.
Cheers everyone.