|OK so wireless has nothing to do with anything and you are strickly dealing with dailup.|
Have you compared all the information on the working laptop to the nonworking one?
Consider concentrating on logon account and password information. Also consider the type of transmission like xmodem... all settings need to match in yours to the working one.
You can also go into the modem properties and check a box to enable logging. Read the log so you can see where in the modem conversation it fails. This will give you a clue as to why.