How do you have your system configured?
I have a cable modem. Cable company sends feed to modem I connect from the cable modem to my NIC in my core. I have no router between them. Then from my Core's Second NIC I connect to my Gigabit switch which then connects to all my MD's and other computers.
Ok, well, that helps some.
Your cable box is your connection to the internet and it likely provides your Core with an outside IP address via DHCP. In the pluto-admin area you can likely discover what your outside IP address is. Check Advanced > Network > Network Settings. Top of the screen.
It is very possible that your cable internet provider is blocking port 80 (and other ports) to prevent you from running servers. What you need to do is figure out what ports are available. If 80 is blocked you could always use 8080 instead perhaps?
You should also check Advanced > Network > Firewall Rules.
You need to open up port 80 in here. You might be able to do this easier under Wizard > Security > Outside Access.
Allow outside access to the website on port 80
Allow outside access to the website on port [ ? ]
You can try a scan at Shields Up! to see if any ports on your system are currently open...https://www.grc.com/x/ne.dll?bh0bkyd2
Basically you have two things to look at..
1) Does your cable internet block common port numbers?
2) Are those common port numbers (80 in the case of your web orbiter requirements) open on your core