Resolution: When I download purchased (or even free) software, I always save the downloaded files. I copied the downloaded files to an external hard drive, put the external hard drive on the new computer and ran the downloaded files. The installation went just as if I had downloaded the installation files directly from Cyberlink. There were no previous installations of PD on the new computer, yet the new software installed with NO PROBLEMS. The lesson to be learned here is to ALWAYS, ALWAYS save dowloaded software installation files.
BTW, the Cyberlink Customer Support response was pretty much useless. In effect, they only said " you can install the software using the same CD Key." No details on what procedure to follow.
Thanks to all who responded to my forum question.