I would check to see whether your system is 32-bit or 64-bit. You can do this by opening Start, and then right-clicking on Computer and selecting "Properties". Under the System group, listed under "System type:", it'll tell you if your system is 32-bit or 64-bit.
Using that information, download the iTunes installer to the desktop. You'll want to download the x86 version for 32-bit systems, and the x64 version for 64-bit systems. Once it's downloaded to the desktop, right click on the installer, and select properties. Under the "Compatibility" tab, check the box stating run this program as an administrator. Close the properties box.
If you were unable to find the compatibility tab or if you couldn't check that box, don't worry about it. Now try running the program. If you were successful in running it as an administrator, the UAC will popup and verify your request to start the installer. Click "Yes" if it does. Hopefully, the installer will work. If not, please let us know and we'll get back to you with more suggestions. =)