because you aren't running a network - you're simply sharing an internet connection. The fact that one of the computers is connected to the router by a cable is of no consequence.
If you have an NTL connection you should have a cable modem connected to a broadband wireless router. The router will then distribute the connection wirelessly to any wireless-enabled computer within range. You may also connect other computers to the router using Ethernet cable via its LAN ports.
This way, neither computer has to be on before the other one can use the broadband connection - the router makes the connection via the modem.