The bookmarks are stored in a file called places.sqlite inside the profile folder. You can copy that file from the old profile folder into the profile folder of the laptop, this will replace the bookmarks in the laptop with those from the desktop.

For details of how to find the profile folder see http://kb.mozillazine.org/Profile_folder_-_Firefox

You can recover more than just the bookmarks, for details see https://support.mozilla.com/kb/Recovering+important+data+from+an+old+profile

Thanks! It took me awhile, but I did manage to get the job done.

Found the places.sqlite file on the old hard drive and copied to equivalent place on new pc. New file shows same size as the old, but not showing the original bookmarks on new pc. Anything missing/not done?