Harry,
Here we go.... This will be a long winded response. The exterior door handles were prone to rusty internal mechanisms, on that model year. I have dealt with this many times. There are 2 ways to go about this. I will list them below.
First way:
Get a can of rust penetrating oil spray (WD-40,.. etc.). One with a spray tube (that little red straw that you stick in the spray nozzle). Insert that straw under the exterior door handle "thumb push button". If you look at the thumb button, there is a gap under it. Spray around in circles, and try to get it all around, inside the door, near the handle. You only need to push the tube in about 3/4 to 1 inch. Now,... beat on the door handle moderately, and then try the push button. If you start to feel the push button getting some resistance, but then it feels like there is nothing there the second time, than this is working. You may have to repeat this many times before the door opens. When you get resistance on the full stroke of the push button, you have fixed your problem. Beat, spray, push the button.
The thumb button is not connected to the "open door rod". The button is spring loaded and merely pushes a lever that is attached to a rod. That lever is stuck in the "open" position inside the door due to corrosion. Beating on the door handle helps it return to it's original position, after you have sprayed it with penetrating oil. This is also the reason you can't open the door from the inside. It's like someone is pushing the button on the outside, when you try to unlock the door from the inside. There is a mechanical conflict.
Second way:
Remove the door panel. This is easier if you remove the back seat. This way you have room to swing the bottom of the door panel upwards. Then you can get at the lever at the exterior door handle and move it back.
GMdude