HT1926 Can't install or uninstall the latest version of iTunes

Question

Everytime I go to install the latest version of iTunes I get through most of it, then a window comes up that says "Windows Installer" - "The feature you are trying to use is on a network resource that is unavailable." - "Click OK to try again, or enter an alternative path to a folder containing the installation package 'iTunes64.msi' in the box below."
In the drop down dox below the previously stated there are two options:
     1) C:\Users\"Username"\AppData\Local\Apple\Apple Software Update\
     2) C:\ProgramData\Apple Computer\Installer Cache\iTunes 10.5.0.142\
Neither of them work and I get the message: "The path 'C:\ProgramData\Apple Computer\Installer Cache\iTunes 10.5.0.142\iTunes64.msi' cannot be found. Verify that you have access to this location and try again, or try to find the installation package 'iTunes64.msi' in a folder from which you can install the product iTunes."
There is an option to Browse for the porgram but I can never find what it needs. Even when I attempt to uninstall iTunes I receive the same messages as above. I have a Windows 7 PC.  I have looked through all the possible Troubleshoots on the Apple website and on the iTunes site and none of them helped. My iTunes works perfectly fine and does everything it is supposed to except when I attempt to install iTunes.  I have tried every way possible and still nothing works.
Below are the windows that appear when I attempt to install iTunes.  Any help would be appreaciated, I just really want to get the latest version of iTunes on my computer, it has been a while since I have.

Answer 1

Superb detail, thank you.
(1) Download the Windows Installer CleanUp utility installer file (msicuu2.exe) from the following Major Geeks page (use one of the links under the "DOWNLOAD LOCATIONS" thingy on the Major Geeks page):
http://majorgeeks.com/download.php?det=4459
(2) Doubleclick the msicuu2.exe file and follow the prompts to install the Windows Installer CleanUp utility. (If you're on a Windows Vista or Windows 7 system and you get a Code 800A0046 error message when doubleclicking the msicuu2.exe file, try instead right-clicking on the msicuu2.exe file and selecting "Run as administrator".)
(3) In your Start menu click All Programs and then click Windows Install Clean Up. The Windows Installer CleanUp utility window appears, listing software that is currently installed on your computer.
(4) In the list of programs that appears in CleanUp, select any iTunes entries and click "Remove", as per the following screenshot:
(5) Quit out of CleanUp, restart the PC and try another iTunes install. Does it go through properly this time?