I get Profile Missing error message when trying to reinstall Firefox

I am trying to simulate a laptop that has never used Firefox and so can't say that "Your Firefox profile cannot be loaded.  It may be missing or inaccessible."  I uninstalled Firefox using the Installed Apps page. Can there be fragments of Firefox that I need to hunt down and remove? I also removed the Old Firefox Data folder from the desktop.

I followed the advise and removed all the profiles from my laptop. (Copies are on an external hard drive.) And I used the download file from the Mozilla community site which is 490 KB versus the 375 KB download file from firefox.com just in case the smaller file was corrupted. But I still got the Profile Missing error message. I am trying to simulate a laptop that has never used Firefox and so can't say that "Your Firefox profile cannot be loaded. It may be missing or inaccessible." I uninstalled Firefox using the Installed Apps page. Can there be fragments of Firefox that I need to hunt down and remove? I also removed the Old Firefox Data folder from the desktop. How can I successfully install Firefox? Then I will use my old profiles that contain all my bookmarks.