Even though you can’t see it, will it let you uninstall it??
If it will, first check if the C://Program Files (x86)/iTunes folder still exists. If it does, is there an iTunes shortuct in there? It my be that only the shortcut has been deleted. If it isn’t there, find your iTunes library files (Usually in your Music folder for your User unless you moved it yourself) and rename the library file (iTunes Music library.xml or iTunes Library.xml) as something else so that it isn’t overwritten when you re-install it.
Then, uninstall iTunes (if it will let you), then run C-Cleaner (https://www.piriform.com/ccleaner/download), and run the registry cleaner. This will get rid of any remains in the registry of iTunes. Then re-start and run it again.
(Running the normal cleaner won’t help the iTunes but it will make your PC go faster – just check all the tick boxes are ticked to your preferences. the default settings aren’t great..)
Then re-install iTunes, run it, and then replace the new “iTunes Library.xml” (or “iTunes Music Library”) with your old ones, with the same file name as they had before. Then, hold shift whilst launching iTunes. Select “Choose Library” – pick “iTunes Music Library” if have that file, “iTunes library” if you don’t. (This is as Apple changed their system a couple of years ago).
That should have fixed it..
bob6397