Cannot close iTunes by any method, Force Quit or otherwise.

Well, it's hard to know why it's choking in the first place. So, the first two things I would try are:

Delete these files in the /Home/Library/Preferences/ folder:

/Home/Library/Preferences/com.apple.iTunes.eq.plist

/Home/Library/Preferences/com.apple.iTunes.plist

/Home/Library/Preferences/com.apple.iTunesHelper.plist

Delete this folder in the /Home/Library/Caches/ folder:

com.apple.iTunes

If your /Home/Library/ folder is not visible then do this:

Open the Terminal application in your Utilities folder and paste the following at the command prompt:

chflags nohidden ~/Library

Press RETURN.

Restart your computer then see if the iTunes problem is fixed.

Have you tried using Activity Monitor in the Utilities folder? If not, then open Activity Monitor; set the Processes dropdown menu to All Processes. Locate iTunes in the list and select it. Then click on the Quit icon in the toolbar. Click on the Force Quit button.