2001 Chevy Blazer 2001 Blazer Doors won't shut. Take two!

The latch stays shut. It looks a little like a letter "c" but with the closed end facing the vehicle itself, so the door essentially bounces back when someone tries to close the door. I have tried to manipulate it with the door handles, the locks, and even a screwdriver without success. There is a little bit of front-to-back give within the slot, but it doesn't want to move back into position. This is true of the latches on both sides. (I assume we are talking about the small black piece that is in the hole and not something further in the door itself.)

I have read on another site that on at least two other Blazers from the same time period, the latch somehow had broken off from the center post inside the door due to a manufacturing defect. I don't know if this is the case or not.