Does iTunes still exist in the Programs & Features control panel even though you've removed all traces in Program Files?
If it is still listed if you try to select and remove it Windows may offer to remove the entry as no longer required.
How familiar you with RegEdit? I suspect you have a couple of keys left behind to the iTunes installer and the Windows Installer Service is trying to use these to remove the old copy of the software before the new copy is installed, but the old installer isn't where the registry says it should be. If you confident using Regedit you could run it from the start button, search for "iTunes64.msi" in values. Export the key it is a part of, then delete that key and try again.
If that sounds daunting then perhaps the Microsoft Program Install and Uninstall Utility can force through the installation, or you could try the steps listed in the the section Install missing components which I've explained a little further here: Re: iTunes Error 7 (Windows error 193), or you may need to use a registry cleaner like the free version of CCleaner.
tt2