To find the serial key for software which you ahve previously registered, go to your Magix account, log in (hopefully you can remember your registered email address and password) go to My products and find the listing for your software.
One important caveat: depending on which operating system your new computer has and given that ACL 12 is now very old software, it may not run properly even if it will install.
@Timothy-Gerry The upgrade to the newest version, Sound Forge Audio Cleaning Lab 4, only costs $15 during the November sale. This might be worth the investment.