It is always possible that the router's built-in Network Switch (the four LAN ports) has failed, so that you can only connect to it "wirelessly".
Try performing a "hard reset" to return it to the factory default settings and then set it up again from scratch and see if that sorts it.
>>> I have also disconnected the Linksys router to
>>> connect straight into the virgin modem by
>>> Ethernet and still get limited or no connectivity.
Did you follow the correct procedure when swapping the connection to the Cable Modem? You need to power everything off, including the Cable Modem which must be left without power for several minutes, so that it loses the association between the existing connection (recognised by its MAC address) and the IP address it has allocated. When powered on, it will recognise a new connection and allocate a different IP address to it.