Are you connecting the Advent laptop with one of the cables from either the Desktop PC or the Dell laptop or are you using a different cable? If you happened to be using a "crossover" cable instead of a straight-wired cable, you would get the "Network Cable Unplugged" indication.
Some routers have a LAN port that can be toggled between a standard LAN port for PC connection and an "uplink" port for connection to additional network hubs/switches. There is usually a button to press to change the setting. The effect of changing this setting is identical to swapping betwen "crossover" and "straight" cables and if you happened to use this port wrongly set, you would also get the "Network Cable Unplugged" indication.