Father of 5 is on the right track.
BUT..here is another suggestion. If you don't see the CLSID key under the QuickTimePlayer.Lib even after you change the permissions, look closely. In my case, after I changed the permissions to all administrators, it only showed my daughter as the one administrator that had permission AND the CLSID key didn't show up at all.
I had my daughter log in. I went to the registry and....low and behold....the is the CLSID key! On a whim, I then tried to download Itunes. Worked like a charm.
I think my daughter must have downloaded a newer version and for some reason, the Apple changed the registry so that it limits who can upgrade Itunes at a future date. My guess: If you don't have permission, log into your computer under a different account and try to install Itunes. I'll bet you a nickel, you'll find one of the accounts works!!