Have you installed the drivers for the laptop in the same way as for the desktop i.e. connect/disconnect the modem as requested?
I used to use my mate's laptop with my former Tiscali BB service and it worked just as with the desktop. All I had to do was swap over the USB cable.
You can get the latest Sagem modem drivers from:
(W. 3.0.4b) Select Tiscali from the list when you install the new drivers.