I am not with Laminar Research; just a flight simmer from downunder.
It is always dangerous to announce your private email address in any forum.
In relation to your problem you need to make direct contact with Laminar Research at email@example.com or at firstname.lastname@example.org In doing so you need to provide full details of your purchase including when and method of payment so that they can trace your original purchase.
As it is now the weekend don't expect a response until it is Monday in the USA. In the meantime I will send you a private message, provided your registered email when joining this forum is the correct address, on an alternative method of possible recovering the product key.
Good luck in solving your problem