If you are getting an error message in the laptop that the "signal" is very weak, you must be attempting to get online via its "wireless" connection which you haven't set up. A wired ethernet connection wouldn't give a signal strength indication.
<<< By the way I have tried connecting the laptop to the modem by itself with the desktop disconnected but no joy >>>
Unless you are using a router, you couldn't have both computers connected to the modem simultaneously. Only the first computer to connect would get an IP address from the ISP and be able to get online.