Rob, others,
For CS6 (as for CS5 and CS5.5), registration with Adobe forms part of activation, so none of them can be run without Adobe having your registration number.
So they must have it, and you must be able to get it, through your Adobe ID, or if that has changed through some other information such as name, email address, or something.
You should be able to get help one of these places if needed,
Serial number and activation support (non-CC, chat open between 5AM and 7PM PST/PDT on workdays)
http://helpx.adobe.com/x-productkb/global/service1.html
Adobe ID and registration support (non-CC, chat open between 5AM and 7PM PST/PDT on workdays)
http://helpx.adobe.com/x-productkb/global/service-c1.html
Adobe Support (phone),
http://helpx.adobe.com/adobe-connect/adobe-connect-phone-numbers.html
or I can alert a forum staff friend that may alert the right someone to deal with it.