I don't know when it happened but QuickTime is now working on my Windows XP x64 system. Even though the last attempt to install iTunes gave a warning message saying the install was unsuccessful I guess that the QuickTime install was good. So, rejoice every who enjoys using QuickTime on a 64-bit system.
Of course, VLC does a better job with fullscreen, but it is nice to have more software working correctly on my system.