I had to restore my 3Play and therefore needed to register online again.
Unfortunately this time another product ID was shown than on my first registration. Therefore I got an error message saying, that this serial number is already registered.

Solution: On my first registration I had the 3P-10 console connected, at my second registration not. After connecting the USB console and restarting the system I got the product ID I knew already and therefore could enter the same activation key like on first time (which can be found on your "my products" page on newtek registration website)!

Might be helpful if someone comes into same situation...

Best regards,