Boot an Ubuntu/Knoppix CD and see if that can access internet or not - if it can, it might be a Windows issue

What random "security" tools are installed, one of them might be blocking access
What error messages does she actually get though? If both your mum's and your PCs are Windows, you could try "ipconfig /all" in a cmd window and compare settings for DNS servers and Default Gateway

If it's OSX, I'll assume the linux shell command "ip addr" works, but you have to decode the information a bit yourself

Try pinging the default gateway, if that works, try pinging various websites and see what happens
yp is just a different server in that domain - www is not mandatory at all for websites