@Sam-Brooks Go to Magix.com and use your old e-mail and password to log in your user account. Then change your e-mail in your user account. After that you should be able to register the product with the new mail address.
Given the age of your product I am unsure of whether it will run successfully under any recent build of Win 10 (assuming that is the OS you are using).
However, there is no real need to re-register the product. If you go to your Magix account, log in and go to User Data you can change your registered email address, which should automatically update the registration details for the app.