Can you recall the exact error message?
Were you able to access the router's configuration pages by typing http: //192.168.x.x (different numbers for different routers ) into the IE address bar? Were you instructed to put in the correct log-in details for your mum's internet account during the phonecall to BT?
Did they ask you to try [email protected]` as the username?
Start menu/Accessories/Command prompt, type `ping bbc.co.uk`, if you get no `lost packets` you are connected to the net, although if the Internet light is off it's unlikely that will work.
From all that , it sounds as though the error during the software installation is what is preventing things working.