Basically, I think that if you are running an internet server, it should tell you if your server is dead, this would be good for newer players who haven't completely gotten a handle on running a server. I just feel really bad when I am choosing a server to join and someone named their server "Please join, no one likes me :(" and it is dead and they probably don't even know that it is dead.
So I think it should just say something in a box when your server starts up like this "Your server is dead. Please check your internet connection and Security settings." Then you can click "continue", "close server", or "check again". Then in blue on the bottom it should say "Have you tried port forwarding?" and it should be a link to the tutorial on port forwarding.