Uninstall iTunes first:

Open your Applications folder, and drag iTunes to the trash
Restart your Mac and empty the trash to ensure iTunesHelper is not running and not installed

Go to your Music directory and open up the iTunes folder
Move iTunes Library.itl and iTunes Music Library.xml to your desktop

Install the version of iTunes you've been trying to install

Open it up, and go to File > Import
Choose the iTunes Music Library.xml that's on the desktop
This should rebuild your library/playlists

You can now delete those library files on the desktop
You should be good to go