ok from your answer I'm 99% sure it's a routing issue
Basically if you have an internet box and you are able to connect several network devices on it without issues, then your internet box certainly acts as a router. You should check wikipedia or google to learn a bit about it.
In a few words, in the case of a home internet connection, the router is there to dispatch packets to the appropriate computer/device connected to it. From the outside of your home you have only one visible IP address: the one of your internet box. If from your computer you connect to a website, when the website returns packets to you, it's the router's job to forward these packets back to your computer and not to the other devices ( mobile phone, tablet ... ) that is also connected to internet.
When the request is initiated from you the router is able to identify the packets coming back and forward them to you ... but when the request is initiated from outside your home, the router has no way to know if the packet should go to your computer, your mobile or your tablet.
That's why you need to forward ports: you configure the router for it to know that if it gets a connection on port 7777, then it should forward the packet to your computer ( identified by your IP address ). It's that simple.
Also to do this you have to be sure that your computer has always the same IP address in your local home network. If you get an IP address automatically ( via DHCP ), there's a good chance that your internet box acts also as a DHCP server. In this case you should configure it as well to always return the same IP address to you ( for your MAC address ).
Hope this helps