The actual source video files, images etc., along with the Photostory project files which you have previously used in one or more PS projects need to be copied to your new laptop if you wish to have access to them there. You cannot copy just the project files since they contain no actual video or images, just a series of instructions which tell the program exactly where to find a given source file on the original computer, how much of it is to be used, with what effects, etc., etc..
Perhaps the easiest method of moving your files from your old to your new computer is to use a USB Memory Stick of a suitable size. Copy ALL the relevant files from your old computer to the memory stick, eject the stick, plug it into your new computer and copy ALL those files to its hard drive. If you want to simply open and load any of your old projects on your new computer it is essential that ALL drives, folders, directories etc are named EXACTLY as they were on the old one. because that is how your existing PS project files will have saved their locations.