I would imagine you can simply install PM on your new computer from "My Account" at the MM web site (unless it is a vintage version only available on CD/DVD). You would then have to de-authorize the version on your prior computer and authorize the newly installed version.

Open PrintMusic on the old computer and de-authorize it.

Download the installer from your User Account. After you install it on the new machine, you will authorize your computer. You will need your serial number and email address on file with MM. 

if you don't remember or can't log into your user account, let MM know through the Submit a request link above.