Answer|Solution:
Additional Details: This new site (new domain name) was restored/cloned from a backup of an old site (different domain name).
Deactivated all plugins except for BPS Pro. The BPS Pro Activation Key request was successful.
Note: When migrating/importing/cloning a site in this type of scenario it is important to deactivate and reactivate all plugins. The reason for that is plugin option settings in the WP Database may still have old values/data saved for the old site. Deactivating and reactivating plugins should update plugin option settings in the database. It may also be necessary to resave plugin option settings in some cases.