Music in folder, but not in library

I recently got a new iMac and moved my iTunes library from my old iMac. After trying several different ways of moving it and not having things link up or appear as they did on my old computer, I finally got as close as possible when I did an "Import Playlist". Things appeared fine until I noticed many (half!) of the songs were missing. Not unlinked with the little "!" next to it, just simply not listed, even though they are in the iTunes music folder. Again, I have tried many different methods of moving it, including moving the entire iTunes folder as Apple suggests, but I continually have files not link up, and not relink automatically after finding one. I don't want to just import everything again. What is the best way to mirror my old library on my new computer. (Incidentally, my old computer is a 2009 iMac running Mavericks, and the new one is the 5K running Yosemite.)