Logging in requires you to use the same email address as you used to buy the software and so set up your Magix account and the correct serial key for the exact version and edition of MM you have. Are you certain that these two requirements are being met when you attempt to log in?
When you enter these details but login fails, what error message do you see? Please take a screenshot of it and post it here or at least tell us the FULL wording of it.
Have you checked whether your computer is allowed (by your firewall and/or antivirus) to contact the Magix servers for verification of your licence for the software?