If you're getting the "The product key is invalid." message please check that the product key is entered correctly. If you type it out instead of using copy/paste, make sure to activate caps lock before you start typing.
If you're getting the "The product key has already been registered." message when trying to register your plug-in on the xlnaudio.com website you have already registered the license to an XLN Audio account. As soon as the product key has been used to register the product(s) you no longer need it, the license is now registered to your XLN Audio user account and available in the XLN Online Installer when logged in with that account.
After registering the product key you'll need to run the XLN Online Installer to download, install and authorize your plug-in:
http://www.xlnaudio.com/install
If it's still not showing up it's possible that you've created two XLN Audio accounts and you're logged in to the XLN Online Installer with a different account than the one you just registered your product key to. If this might be the case, click on your email address/the person icon in the top right corner of the XLN Online Installer and select "Log out from the Online Installer", then log back in with the account you registered your product to (check which account you're logged in to on xlnaudio.com if you're not sure).
If you have rented your XLN Audio plug-in through Splice and ran the XLN Online Installer during this period, and the product is listed in the XLN Online Installer but not authorized even after registering the product key, you might have registered the product key for the paid off license to another XLN Audio account of yours.
If you realize that you've registered products to two different XLN accounts please get in touch with XLN Audio Support and we'll help you merge your accounts.