PROMBLED SOLVED: I found the upgrade (patch) for LR6 to LR6.1 and it fixed the problem of (Not Responding).
Here is the Adobe website: http://blogs.adobe.com/lightroomjournal/2013/06/keeping-lightroom-up-to-date.html#rcc2015
Scroll down about half way on that page and select "Lightroom 6 (the same links works for Lightroom CC)". Below that choose the link "Lightroom 6.1/2015.1" (this is the Windows version for me). This will begin the download. Be aware this is not a full install LR6.1, only a patch to create 6.1. So you must have installed your Lightroom 6.0 prior to all this even though it's not functioning (Lightroom Not Responding) AND don't launch it. When the download completes, you'll see it's a ZIP file. I personally moved this file to a folder calling it Lightroom Upgrade to 6.1. Unzip this file. Next look for the folder "setup", and open it. You will next see a red icon with the file name AdobePatchInstaller.exe. Double click this file and watch it operate for about a minute to conclusion. DO NOT LAUNCH your Lightroom; instead immediately reboot (restart) your computer. Now launch Lightroom and Voila !! It works. Also notice on that Adobe web page these same type of files exist for previous versions.