without being able to reproduce, thers not realy something I can troubleshoot.
could be any number of things really.
try running the session test file from this post on the laptop:
http://www.webassist.com/forums/showpost.php?p=23826&postcount=2
it could be that the laptop has a session management problem. impossible to tell, really, without being able to reproduce on my end.
at the end of the day if it works on the live server that is end goal right?