[MovedGoalPosts]

Ok, not totally familiar with your Linksys WAP, your user guide may give some clues.

With a hard wired network you would usually have an arrangement of:
modem / STB > router > computers (clients)

[between some the router and client you can add the WAP]

With your wireless network your arrangement will be:
modem / STB > WAP > Computers (clients)

Now if your WAP can support more than one client connected to it at a time, you might just get away with it. If you need to pass files from one client to another, your WAP may not allow this sharing facility and need a router or switch. Additionally a WAP will rarely assign internal client network IP addresses or similar functions, yet routers often can.

Most modems or STBs that ntl offer allow only one physical connection to a client at a time. If you try to share the connection without some form of router capability, only one PC will work. Inevitably you have to keep rebooting your modem/STB every time you change computers.

The router takes care of the sharing capability. The modem/STB effectively sees only the router connection and thinks that this is the only thing asking it for internet access. Gizmos in the router work out what client is trying t send and recieve what data and where that enquiry needs to go, whether from the modem/STB or to another client.