I went to Apple Genius at the King of Prussia store in Pa. I must admit that I was very impressed with the all the people that I dealt with. Four Apple Genius people helped me get all of the master photos restored. This involved Apple Genius people who either specialized in the iMac or Aperture. Each person brought additional pieces of the information to forefront. The Aperture specialist was able to trace the pathway of the photos and locate where the originals were located. We then set up a new Aperture library and moved all the old libraries (there were more than 1) into the new library. I had brought with me two external hard drives, one that I had used for Time Machine and the other for general back ups. The new library was placed on the general back up drive. Remember that there were about 9000 photos. The total time I spent at the Apple store was four hours.
They were also able to delete the Time Machine files that I had dragged to the trash but would not delete. They used the Terminal program that I believe was listed in another area in this group. (I was also told that Time Machine will delete files on its own and just let it do that.) I had also listed my external drive to not back up on the Time Machine drive. This was also changed as we moved the Aperture library to that drive. Now Time Machine will back up all Aperture files.
I still don't know why the files had lost connection with the originals but everything is back working again. I had been keeping vaults and Time Machine but the previews could not locate the originals.