If you are installing to an external HD that you intend to be portable then you should download the zip or 7zip version and extract the xampp folder so you have for example C:\xampp on your external HD.
DO NOT run the setup_xampp.bat file as when you go portable you don't want any paths configured as they may not be the same when you plug the drive into another PC.
Here are some instructions that may help you uninstall and then install using an archive version:viewtopic.php?p=179699#p179699
Try and return your Ext. HD, your desktop PC and your laptop to the state they were in before installing XAMPP.
The installer version is not portable and is perhaps why you are having problems when you plug it into your laptop.