After reading some of the suggestions, I deleted every reference in the registry to quick time -a very tedious process- and used the search function to find any other files that included quick time and deleted them. At that point I only had one .cab file (that couldn't be removed) on my boot up drive that had anything to do with Quick Time. All that work turned out to be an exercise in futility as the latest Quick Time program still would not install because it couldn't remove the old version???
My next step was to install an older version of Quick Time (2 versions back). That installed OK, so then I went to update it with the next newer version. During that install, I got the message that an older version couldn't be removed. So I clicked on OK and the installation process then continued right through to the end! Figuring my luck had changed, I then went to install the latest version, and the same thing happened - got the error message, clicked OK and it went right on installing the newest version.
Ain't computers (and software) fun!