You need to deactivate previous registered installations. To do this, go to your Magix account, log in, go to My products and find the listing for whichever version of Music Maker you wish to use on your new computer.
Click on the Show more details link and you will see a list of all currently registered activations. Deactivate any you no longer need. You can also check there that you have the correct serial key .
Log out of your account, allow a few minutes for the changes to be active and then try again to register and activate your new installation.