My CS6 backed up application, when restored, doesn't work.

Being perfectly satisfied with version CS6 of Illustrator and my Mac mini, I was as happy as Larry!  Trouble is, that after a recent crash, I relied on my external backup drive to restore everything back to normal. 99% is fine BUT my Illustrator CS6 doesn't work.  I do have version CS5 installed as well, but I'm now unable to read or edit any of my old files. On my back-up, are the installers, but they require the serial numbers.  Originally, I tried to upgrade from CS5 to CS6, but at the time Adobe said it was too late and the upgrade had been discontinued. So I went on the illustrator forum to complain. I've been a loyal Adobe customer for years, since Photoshop 4 and Illustrator 6 and have a printed out copy of my purchasing history.  An official Adobe administrator, contacted me as a result and allowed me to download the CS6 installers. He even phoned me and I followed his installation instructions. All my other purchases are on CDs with serial numbers on the cardboard sleeves. I have a Mac mini with Mountain Lion installed and, as a retired person, I don't want the expense of upgadig my hardware and pay the perpetual rental/subscription for the  latest versions of software. As a cartoonist and comic strip artist, my CS6 version is all I need! Help please.