<<< Once I'd copied to IP address from the PC it connected. >>>
I don't follow this. The laptop should get its IP address automatically by DHCP from the Livebox. If it fails to do so, Windows will default to allocating a "169.254" address, which won't let you access the Livebox or get online.
If the adapter isn't connecting properly to the Livebox, allocating fixed addresses hides the fact and everything looks OK, but it won't work.