Cannot move Parallels to new computer -- product key problem

I have Parallels Desktop on my macbook and an imac. When I log into my account, the macbook version appears, but not the imac license. So I cannot deactivate the imac license to move it to a new imac. When I try to activate Parallels on the new imac, and put in the proper license key, I am told the product key is registered to a different account, and cannot be activated on the new computer.
I have tried using my two other email addresses to figure out to which the product key is attached. Because I don't have any record of the login, I have attempted with each address to reset the password. I get no email in either account to reset the password, so I assume there is no account for either email address.
I have an email receipt for the purchase, including the product key, but I can find no way to log in and deactivate it. I also can find no way to contact Parallels directly to fix this problem.
What must I do to fix this???

 

Hi @RobertB40, could you please share your key with us via the private message, we will check it for you and help to activate on new computer.

 

Dear @RobertB40, we've recieved your email and moved your licenses to m*di*******dc@gmail.com
Please check.