How did you reinstall Lr; from media or a download from Adobe?
Do you have a Creative Cloud subscription?
No. I purchased the program outright.
What LR version license key do you have? i.e which version was installed on your computer previously?
If you are trying to activate the latest version LR 5 a license key from an earlier version e.g LR 4 or LR 3 will not work.
The original was 5. The one I was attempting to reinstall was 5.
Adobe helped, but it took 5 minutes between responses after waiting 45 to get an initial reply. It only took 6 hours for them to resolve. Apparently Lr thought I had a subscription instead of a stand-alone purchase, and so was confused. Pretty sad.