You won't be able to apply the licence if it can't connect.
If you have any VoIP trunks, they will won't show as registered if there is no connection.
You should be able to log into the system from another PC if it is connected to the LAN. You should be able to determine if the LAN has an internet connection using the computer you logged in with.
If this is a Windows system, you could use a number of other programmes, on the 3CX server, to see if you have a connection.
There is nothing that turns green to indicate an internet connection.