Please contact the author of your purchased theme, the theme author will assist you (assuming theme author has a database system to keep record of the license).
How to contact an author to get support or for any technical query:
To use purchase code again which already used for any website (mean theme license already registered) you have to unregister/deactivate the theme license from the old domain/website. you can not use the same purchase code for more than 1 website.
If you don’t have access of old website wp-admin where the theme registered/activated then you have to contact theme author and request them to unregister/deactivate the theme license from the old domain/website.
You can post a comment in the theme Comments page and let them know that you are waiting their reply. Hope theme author will assist you.
I have access of old website wp-admin where the theme registered/activated. How can I remove it from wp-admin?
Note: I already removed the theme from my old site.