I have changed my computer and transferred files. It was then necessary to download a replacement for web designer. Since I have an account already I assume that I do not need to purchase again but I cannot find my product key.
Welcome to the Magix user to user forums, so not a contact for any Magix staff and we do not have any access to your account details and serial keys.
It is the user's responsibility to keep a careful record of all product keys, serial numbers etc., but, since you say you have a Magix account, go to this page, log in, go to My Products and find the listing for your version of Web Designer. You should find your serial key there. You should also see the number of activations currently listed for the software on your account; it is a very good idea to deactivate any that are no longer in use.