Initial setup, Roku not connecting to the Internet, Router settings.
This post is for the first time user, if you have just replaced your router, as well as the Roku developer.
If you have tried everything else and are still having Internet connectivity issues, look at your router's security settings. In my case it was “access control” which denied access to non-registered devices.
Roku's on-screen messaging gave no indication of that specific issue, it was only after I tried to connect an old, no longer used laptop which indicated that my “Router denied access”. So if that's your issue, it just a matter of logging into your router and changing it's configuration. Check your router's manual for those procedures.