Thanks to everyone for the valuable advice, I'll let you know if I have success when I try to reinstall on my other computer (hopefully later today).
Update: I found my LC program in my C drive under 'Radium Technology'.
I removed the program.
Then I downloaded the trial version of LC15 and re-entered my license keys.
Then restore my latest backup.
Voila! Everything is now back to normal and it wasn't the huge disaster I thought it was.
Now I'm just thinking I need to find a replacement software for LC since it doesn't seem to be supported any longer. I'd appreciate any suggestions for that replacement would be appreciated.
Thanks for you help!