I had this problem, after I uninstalled the previous Lightroom installs I had, Lightroom 6/CC was available but it did not work at first. I was able to fix it by editing the Windows registry (it was only a minor edit).
I changed the value of the following registry key:
The value was:
C:\Program Files\Adobe\Adobe Photoshop Lightroom 5.7\Lightroom.exe "%L"
I changed it to:
C:\Program Files\Adobe\Adobe Lightroom\lightroom.exe "%L"