I rebooted it this afternoon when all of this started.
I run Windows 10 version 1709
I looked back at the update history and it had a windows feature update on Jan. 2nd
As well as a Security update of Feb. 7th. I know I last used LR sucessfully 5/6 days ago, so that timing is suspect to me.
It specifically says:
Summary
This security update resolves vulnerabilities in Adobe Flash Player that is installed on any supported edition of Windows Server Version 1709, Windows Server 2016, Windows 10 Version 1709 (Fall Creators Update), Windows 10 Version 1703 (Creators Update), Windows 10 Version 1607, Windows 10 Version 1511, Windows 10 RTM, Windows Server 2012 R2, Windows 8.1, or Windows RT 8.1.
Then I suspect the Windows update did something to the registration file folder location. Like changed the permissions on it.
You should reinstall LR right over the top of the current install.
You can download the Base Installer and the 6.14 update from here.
Download Photoshop Lightroom
Make sure you download both the base installer, Top, and then the 6.14 update from the list below.
Install the base installer then update it with the 6.14 download.