not a new connection no, she is on talktalk has desktop and one of their modem boxes....
its just weird that I can plug the Belkin in in my house using my phone to Belkin lead and get a world icon green light but not when I try the same in hers....I don't think there is anything wrong with the hardware, will take my leads over tomorrow and try that.
Just how has she got this set up? Am I right in thinking that the desktop is connected via the modem, and that you are trying to connect the laptop wirelessly via the router? I think that they should both be connecting via the router, but somebody will tell me if I'm wrong.
So that's not a wireless connection is it? You cannot have two different connections to TalkTalk on two separate phone points.
The PC needs to be connected through the Belkin router into one of the phone sockets. Then the laptop has to connect wirelessly from the lounge to the Belkin router in the study. You don't need (in fact you can't use) the existing modem so remove it from the equation.
In answer to your last question - yes it will interfere with the router as I've explained.