For a couple of hours there I thought I had it figured out.
OK, here's the deal. The modem she has is a 4 port Billion Bipac5100, which has an RJ11 socket, and the lappy is a Dell Inspiron 1200 which is eight months old. I now remember that when I was discussing the configuration with her prior to order we decided not to get a wireless card as an option because she didn't have a wireless modem. So now let me see if I've got this right.
Option 1 is to buy a wireless router and a Wi-Fi card (sorry tinny, you lost me; are those Belkins I linked the Wi-Fi card we're talking about?) She installs the card, plugs the modem into the phone socket in the kitchen, and plugs the router into the modem. Now once properly configured there is no need for her laptop to be wired to anything configured she should now be able to use her laptop anywhere within range. Yes/no?
Option 2, slightly more expensive, is to buy a wireless modem/router and Wi-Fi card. Her old modem is unnecessary, the modem router plugs directly into the phone socket, configure, and Robert's your father's brother; wireless connection anywhere within range. Yes/no?