I would venture the guess that you cannot have two versions of iTunes running at once, especially if they're sharing component files.
My advice would be to delete both versions. Re-install the new version (should be easy enough to find, if you have a new system). I'm hoping for you that you still have access to and have iTunes installed on your old Mac. If so, go into Music, through Finder, click through the iTunes folder(s), put all your library files in a folder, burn them to disc or drag them to an ext. hard drive or upload to a cloud or dropbox, since your previous machine is pre-cloud. Dropbox.com creates a cloud like interface. Then you can drop the files directly into iTunes on your new Mac.
I hope that would work.
Let me know if that made any sense to you and how it worked (: