It may be that you can't get two registrations / licences with one e-mail. Since the registration requires your product id, it's possible that you can only register it once, no matter how many e-mail addresses you have, no matter how many computers you have. Thus, new attempts to register will fail. An attempt to transfer registration data from one computer to another might be held as a violation of copyright / user rights, as such it would be illegal - not trying to paint any spooks here, nor blaming you, just giving possible facts.
The only place to know this for sure is the support of the manufacturer. Do contact them. Best wishes.