That sounds like you haven't forwarded the ports. Port forwarding allows access to internal services from the internet - so the fact that you can connect inside of your network but not outside sounds like this is the issue. How you forward ports is different by router make/model but if you visit www.portforward.com
and search for your router make and model there will be instructions on that site.
Basically, for each internal port, you need to forward it from the outside world;
So for SABnzbd - the default port is 8080 - so you need to open up port 8080 on your router so that when a connection from the outside world tries to access port 8080, it is forwarded to your internal port 8080. You will also need to specify the destination IP address - so if SABnzbd is running on a laptop with an IP address of 192.168.0.2 then you would forward port 8080 externally to port 8080 internally on 192.168.0.2.
All this will make much more sense when you log in to your router.
If you need any more help, post the make and model of your router and the internal
IP address of the machine running SABnzbd and I will try to help you.