How can I get past the "serial number is already associated" error starting X6 on my new PC when I have already uninstalled it from my old PC?

I had CorelDRAW X6 on my old PC.

I started CorelDRAW X6 on that old PC, checked the Help menu to confirm that I was signed in, and then closed CorelDRAW (was that my first mistake?!).

I used Control Panel to uninstall CorelDRAW X6 from my old PC.

I started CorelDRAW X6 on my new PC (pre-installed by my employer's IT staff).

After signing in, CorelDRAW displayed the error message:

"We're sorry, this serial number is already associated with an active membership or subscription in your account."

I'm stuck. What do I do now? How do I update my account to "disassociate" that serial number from "an active membership or subsscription" in my account?