The tail gate and rear window will not open although I hear the electric release motor operate

I had the same problem with my 2001 Blazer. Just remove the panel by the screws located on the side of the tailgate, the problem was a bad actuator which pulls the lever to open the glass hatch. Once you take off the panel, remove the metal shield on the tailgate and the actuator will be mounted on the back of it. There are several ways to open the hatch on blazers and jimmys. You can try to release by inserting a small screwdriver and pushing left using the entry hole in the rear hatch deck just below the plastic trim in the center. This works ok unless the latch is out of alignment. The quicker way to release the window lock is to pull the center of the plastic trim (where it rises) toward the inside of the car and break the plastic trim attachment. Remember first to remove the hatch handle.By pulling away from the window, you can then insert a finger between the two walls of the lock assembly and push down. The window will open immediately. Ignore the broken trim attachment as there is plenty of support for the top of the door trim piece. Unbolt the 9/32 panel screws and the two phillips head side screws and the panel will come off. Careful of the rods clipped to the panel. They come off easily as does the hatch door activator. Rather than have to buy an actuator because the blue piece of plastic broke, replacements are available at online auto supply stores. Remember to make sure that the lever of the actuator hits the window release mechanism squarly. A little bending with pliers will align these two pieces so they strike evenly.