You are the admin, that does not mean that you have all the permissions to do everything in the admin account. That is vested to TrustedInstaller, not to Administrator. To run a program as admin means you right click on the program, get the right click context menu , locate the option "run as Administrator" there, aand click on it.
If this trick also fails, you should try to download iTunes once again. If any part of the download is corrupt, these messages occur.