Problem: "When I click the 'OK' button, I get a message that says, 'We are unable to authenticate this registration code that you supplied.'"
Probable Cause: It sounds like Lotto Sorcerer's Apprentice's serial number has changed.
Lotto Sorcerer's Apprentice should "remember" its serial number (and registration status), even through an uninstall and reinstall. But if you reformat your hard drive, or reinstall your operating system, or get a new computer, this serial number can change.
Solution: Request a replacement Registration Code
Use Lotto Sorcerer's Apprentice's menu item "File > Registration > Replace Registration Code" to get a new registration code.