No solutions but some time back I got to the point that I no longer had the ability to uninstall Mozilla and all attempts to install again won't work. I've resorted to using Firefox.
I've noted that in \Program Files\Mozilla.org I have five instances of Mozilla folders possibly created each time I've tried to reinstall over whatever was there after uninstalls failed.
Do you know if I delete all you note if I'll still have everything running fine for Firefox which of course seems to have it's own directory as it should?
I had the chance to get a dead Mozilla. In short, the fix was:
1. Delete \Program Files\Mozilla.org
2. Delete \Program Files\Common Files\Mozilla.org
3. Install Mozilla.
While successful, maybe someone else can narrow down what it was in particular, but it's running now...