Ok. I didn't enjoy this the first time it happened - and I'm absolutely not enjoying it now.
Although I solved the registration/licensing problems described at the top of this thread - tonight, I had to reload the chipset NIC drivers for my server and I am once again faced with an unlicensed copy of Media Center. For the record, I uninstalled the NIC drivers before re-installing - and only updated the chipset drivers (without uninstalling first).
This new problem, along with the original problem which seemed to be caused by installing an exact replica of a failed motherboard, suggests to me that the MC license intentionally, or unintentionally, "breaks" when certain system components in the computer are replaced - or when their drivers are reinstalled. This seems very much like the hardware-based authentication process that Windows uses.
Whatever the explanation is, and regardless of whether or not it is intentional, I am becoming somewhat agitated, and frankly very concerned, that I am using up my allotted licenses unnecessarily, and that I will not have any available licenses later this year to apply to new machines that I plan to purchase.
JimH, I would very much appreciate some feedback on this topic as I am a loyal customer who is blowing through licenses at an alarming rate just to maintain my current system.