Is it possible there's a little bitty bit of whitespace outside of the PHP tags in blabla.php line 581? I bet there is.
See, if you have anything outside of PHP tags, that is sent to the browser. And once something has been sent to the browser, you can't send headers (like the sessionID cookies!) anymore.
The problem is likely not XAMPP, but your PHP code as you put it on the flash drive.