I assume livebox is just some kind of router. If so, check if you have mac address filtering configured on the livebox. If so, you'll need to specify the mac address of the pc to allow it to connect. What security do you have implemented on the livebox? Perhaps you need to specify a WEP key on the laptop.
Well merlin that certainly tells us something about you then I guess. Wireless routers are absolutely no problem, well they haven't been to me anyway!
I've got a livebox traceyh and no problems with it at all. It must be the WEP key as graftarian says. It has to be precise. It will just be a matter of getting the correct settings in your latop not the livebox if your PC is connected ok! There is a booklet that came with your livebox with tips on configuring a wireless network, have you had a look at that?