Depends on the version of Windows you have on the new computer and which version of MEP you purchased.
If it is compatible with the Windows version then you can download it again by going to the Magix.com website.
Click My Account top right of the home page and log in using the email address and password you used to register the software.
Select My Products and you wil be presented with a list of your registered product(s) with download links (providing the version is not too old) and serial number.