For MAGIX released products, sign in to 'My Account' on the MAAGIX website and go to 'My Products' where you will find all your registered programs. Under the serial number for each product, there should be a linked called 'Show more details' - clicking on this will reveal how many activations your are allowed and which activations are currently in place. There is also a 'Deactivate' link under the computer name to which there is a current activation. Just follow the deactivation process and then that should clear things up for the re-installation on your new computer.
If any of your products were from the former Sony ownership (e.g. SoundForge Pro 11 or prior), you would need to contact MAGIX Support via your MAGIX account to request the reactivation limit to be reset. Even though those products should appear under 'My Products', those former Sony products use a different activation system to that used by MAGIX and the reset needs to be MAGIX Support after the activation limit has been reached.
The number of allowed activations for SCS (Sony) versions of SF and Vegas is unknown, but most folks do not come close to the limit which can be reset by Magix. OTOH, Magix versions are limited to two activations at a time.
Always back-up your serials and log-in information. This is cheap and easy with all the free storage sites and email. A Gmail account has both (and more) email and15GB storage. There are other options as well.
btw, welcome to the Magix Sound Forge users forum @Timothy-Hall .