What could cause the turn signals on a 1996 blazer to not work when the fuse is good blinker is good and switch is good?

You can check the battery, but I don't believe that it's the battery. Check the "multi-function switch" You will have to remove the plastics around your steering column. Then, on the bottom side, there is a big black box, attached to your windshield wiper/cruise control lever, held in place with, if I remember right, three bolts. Take those loose, and trace down the wires. They should run under the dash to the left side. There should be one bolt holding the clips together as well as the plastic snaps. You can't miss it. It's probably two inches across and about a half inch wide with probably thirty-five wires. Unplug it, and pull it through the dash and column. Install the new one. Now, you would probably be safest if you unhook your battery before you did all this. Just a precaution. And be prepared to shell out a couple hundred for the part. It's not cheap as it controls your brake lights, turn signals, hazards, windshield wipers, and cruise control. I believe that it runs 180 at Autozone. Good luck, and I hope that I'm not too late in answering this for you.