Yup, that serial number is only for the Personal Learning Editon of Bryce, which was the version previously available as a free download.
THe Current Bryce 7 Pro offer is the fully featured version, but as you have found out, the file is the same. THe serial number is needed to unlock the advanced features.
If you Purchased Bryce 7 Pro actually through the store system, having to go through the checkout, then you wil find a serial number in your account.
However if you used the more recent Download link, which is a direct download, then unfortunately you will have to wait unti Daz3D can email you a serial number, or work out some other way of distributing them, because the Readme with the number was omitted form the download.
Sorry for the inconvenience, but I am sure it will be sorted out soon.