You should be able to use the wireless router.
Install the router software and drivers first, then switch off the PC and connect the router.
Once the drivers have been installed use the information provided by Talk Talk to set up a new connection from control panel, network and sharing.
Follow the wixard to add/make a new connection.
Once you have established the connection and checked it works, set up the other PC in the same way but make sure you use the wizard to make a network connection to your current one. you will need the security key which can be found with the router (sometimes on a sticker on the base). When propted enter the WEP/WPA network key and finish the wizard. now see if you can connect.
Post back if problems...