Unlinking License Key from Old Installation

Good afternoon,
I got a new Mac recently and I'm trying to get Parallels set up on it. I have my old license key, but I don't see a way to unlink it from the installation on my old Mac - if I paste it into the new one I get a message that says "Your product license has reached the activation limit." I've found several forum posts that indicated that this was something support was able to do - could I get some help with this?

I wanted to open a support ticket for this instead of starting a new forum thread, but every time I pressed the "New Ticket" button I was redirected back to the support home page.