I just had this problem and fixed it, but didn't see a solution here so I'm posting the solution here in case it helps anyone...
My wife parked her 1996 2.4L LS convertible at a store. When she finished shopping the shifter (PRNDL stick) would move but the transmission would not shift from "Park" into any gear. (I think that the same situation could happen with the car getting stuck in any gear.)
Diagnosis and temporary fix:
I opened the hood and looked for movement while my wife moved the shifter. I could see that the shifter cable (which has a black-plastic end) had become detached, and was dangling below the transmission's shift lever (which has a metal pin sticking down). It's located just forward of the firewall on the driver's side. As a temporary fix (in order to drive the car home) I was able to put the shift-lever pin inside the shifter-cable cup and then tie them together with a an elastic hair-tie (tripled-up to make it smaller and stronger). That worked and my wife was able to drive it home and put it in park. (The shifter-cable can become detached at the stick-side, so if you have the same symptoms but don't see a problem at the transmission-side, the problem could be at the stick-side.)
When I got home and did some research, I learned that the problem is that a plastic bushing at the end of the shifter cable had broken/disintegrated and therefore it would no longer hold onto the pin that sticks down from the transmission's shift lever. (You can replace the entire cable or just the bushing. I chose to replace the bushing which is cheaper and seemed to be less work.) So I ordered a Dorman 14055 Shifter Cable Bushing. That Dorman package comes with 2 bushings; a white one for the transmission side that I used, and a translucent one for the PRNDL-stick shifter side that I didn't use.
The end of the shifter cable (at the transmission-side) is shaped like a cup with a hole in the bottom. It is a single piece of black plastic (even though it looks like it might be 2-pieces). The inside of that cup has ridge, and the plastic bushing snaps into that cup. The shift-lever pin snaps into the bushing. Replacing the bushing was more difficult than I expected because of the close quarters. I recommend having 1 or (preferably) 2 good lights to shine into the small space. You'll probably want to have a thin, flat-head screwdriver and maybe an awl. You'll need a pliers to squeeze the bushing into the cup. (I put a thin piece of sticky-back rubber onto one jaw of my pliers in order to avoid breaking the cup at the end of the shifter cable, but I'm not sure if that was necessary.) I also ended up using a small length of cord to hold the bushing in place while I squeezed it with a pliers.
1) Be careful not to bend the shifter-cable too much or else it will break that plastic bushing that holds the cable-sheath into the engine compartment.
2) I removed the remnants of the broken (white or yellow?) plastic bushing from the black cup using an awl and a screwdriver.
3) I check the shift-lever pin to make sure that it wasn't holding any bushing remnants. (It wasn't.)
4) I squeezed the white bushing into the cup but this was very difficult because of the close-quarters and limited visibility. It takes a lot more force than I expected and I was afraid of breaking the plastic cup, so I squeezed with slowly-increasing pressure. Dorman suggests putting the bushing into hot water in order to make it softer so that it snaps-in more easily. I tried that but I found that it didn't help because the bushing cooled-off by the time I could get it into place. I dropped the bushing several times on several tries which was very frustrating. Eventually I solved the problem of dropping & retrieving the bushing, by putting a short length of cord through the hole in the bushing and I tying a knot in the end of the cable such that it wouldn't slip through the bushing. Then I threaded the other end of that cord through the hole in the cup at the end of the shifter cable and I clamped a binder clip on that cord about 3 inches below the cup. The cord prevented the bushing from falling-out, and the weight of the binder-clip pulled the bushing into place, thereby making it easier for me to get a pliers inserted such that I could squeeze the bushing into the cup. Eventually I was able to snap the bushing into the cup (and remove the cord & binder-clip).
5) Once the bushing is snapped into the cup, it is easy to snap the bushing onto shift-lever pin by hand, by simply pulling up on it (though you probably want to use work-gloves to avoid getting pinched).
I'm disappointed that the design relies on snapping-in the shifter-pin to plastic bushing that disintegrates with age. I would have expected the connection to be held together with a cotter-pin or something. But apparently this system is used by MANY carmakers on MANY models, MANY of which use this exact same bushing. I guess it saves a few second of assembly-time to have a snap-in system. If you have an old car like mine, you may want to consider keeping a spare bushing in the car along with an elastic hair-tie or something similar.