Login to your account at magix.com - account login icon is top right of the home page - using the email address and password used to register the program, even if you do not have the email address the login will still work.
Under My Products you will find a link to the download and the serial number, under the Show more details option, deactivate the installation on the old computer.
Instal ACL, as normal on the (new) computer, and activate it.
If you have forgotten the password then you will need to contact Magix by email to infoservice@magix.net giving them your old email address and serial number, or order number if you have it, asking them to change the email address and reset your password,
Hopefully, it (your original installation) is already registered from when you first bought and activated it! If not, and you have no other Magix products and hence, no user account, you will certainly need to follow @johnebaker's advice and contact Magix Customer Service.