Exactly what does happen when you try to open Lightroom? If there is an error message, please quote it word for word.
Nothing happens, except the Windows egg-timer flashes for a few seconds then goes away.
You might want to try a reinstall. I am running Lightroom CC 2015 and Photoshop CC on Windows 10, and I don't have any problems with it. You can download the installer from:
This morning I did a System Restore to when Lightroom did last work OK. I tried opening Lightroom, Photoshop and Creative Cloud: none of them worked and they reported a re-install was needed.
I reinstalled the Creative Cloud app, then reinstalled Lightroom and Photoshop from within the Creative Cloud app. They all work OK now.
I suspect that something in my Windows 10 system was corrupted and/or in Lightroom. Now I need to get on with importing a bunch of photos for a meeting this evening.....
Thank you everyone for your help.