Thank you turingtest2, you have turned my frustrations into success. Your 6 step process was what I needed to get my itunes working on my new computer. I have kept the Media Files on an external hard drive and my Preferences in iTunes was pointing to it. The folder with these files also held a library file and the rest of the files needed for the library. I have always thought this was the correct library file. When I copied this folder and pointed iTunes to it when I opened it, it did in fact open a library but it was all wrong. Very old, in fact. Old podcasts I had long ago deleted, most of the new movies missing, not locating a lot of the music, just a mess. I knew it couldn't be right because all the media was there, library had been set to keep media in the itunes library when adding, it was consolodated. It finally hit me to look in the normal place for iTunes library files. There was an iTunes folder in my home directory and sure enough, when I pointed iTunes to open that library all was correct again.
So, I followed your steps to move those files to the external drive and now I have a portable folder for iTunes that I was able to connect the hard drive to the new computer, tell my new copy of iTunes to open that library, and it's PERFECT. I can't thank you enough for taking the time to walk us through the process. Very helpful indeed.