Just adding to this thread years later as this just happened to me and I now know what is going on.
The latch mechanism opens by a cam/lever when you lift the glove compartment latch. Although most of the latch parts are metal, the cam that moves the lever is plastic and the key corner wears out. This lets the cam go too far when you pull too hard on the latch and it gets stuck in this extended position, and the upper toggles are then stuck in the closed position (into the upper dash frame) as the cam lever is not being pushed open by the cam.
You can work the cam loose by turning the key in the latch to vertical (locked) as this rotates the cam and gets it out of the extended position. Then turn key back to left to get to the unlocked position and see if the glove compartment will open now when pulling gently on the opening latch. In my case I needed to push in on the glove box to relieve pressure on the upper toggle barbs so they will release when pulling up on the latch, without going pulling to hard on the latch and getting the cam stuck again.
I can't tell if the plastic cam is part of the lock kit or the internal latch part. The plastic cam fits around the lock cylinder and rotates with the lock cylinder, which is why turning to the lock position frees up the cam.
But I think the glove compartment alignment is part of the problem that causes the upper toggles to get stuck, and then you pull to hard on the opening latch, causing the extended cam problem. The alignment is done by the attachment of the glove box to the rod underneath the glove box. You get to this by removing the plastic panel below the dash and behind the glove box. Just slide the plastic panel forward and it will come off. Then loosen the clamps on the rod to get a better alignment of the glove box, so that the upper toggles don't get stuck when closed.