Your problem might be what opensourceguy suggested or it might be the same problem I have fixed, I posted this a while ago. It sounds like this is more plossible with your explanation of whats happening.
I know the solution to your problem, I have an 89 and just fixed mine. This is very common in the 88 to 91 model. Directly behind the button on the exterior door handle is a funny metal piece that hinges and pushes a rod that leads to the actual door mechanism, well this hinge has seized in the down (or pushed in position) due to corrosion. To open the door make sure it is locked first and then deliver some sort of hard blow to the door this will pop the metal piece back into place (I used a rubber mallet but you might like the appearance of the door so maybe just use your fist) then unlock and it should open as normal.
Unfortunately the problem will persist, so if you want it fixed you must tear your door completely apart and remove the handle to fix it. Their are three solutions to keeping the metal unit from seizing, one is to go to a junk yard and find new/used handles at 10 bucks a piece or you could lube the mechanism (but beware the problem will come back worse) or the best option is to drill out the pin that acts like a hinge, file down the corroded metal and put new bolts in (be sure to use stainless steel with locking nuts). Also it might be a good idea to lube up all the parts of the door mechanism while the door is apart. This is a 2 hour job per door with proper tools and you will get greasy. I am sure a mechanic would charge a handful, so if you are the least bit mechanical you could do it yourself and save.
So I hope this is helpful for you. If you are in the Minnesota area I could arrange to fix them for you for more than likely a lot less than a mechanic would charge. Good luck and if you have any additional questions feel free to ask.