I am clicking the link taking me to my account and that is the same key, it even shows a pop up when I enter the account area that tells me I have registered the site before and gives me the same key again!
Can I get access to your site and I will try and register the site under my account and see if I have the same experience?
I will mark your next reply as private so that I can get log-in credentials from you—you may want to create a temporary admin user for me to use that you can later delete. And be sure to have a current backup of your site, even though I don't intend to make any changes other than trying to register the site.