Rushing – more later if it looks like it might be useful:
I have no experience with this particular camera.
But work according to general principles.
The slots on A and B are locking slots.
A pin penetrates the slot when the door is closed and moves into the locking position under the back of the hand when the door is moved sideways.
The red arrows at A indicate the path that the locking pin on the body would take to unlock it. The door moves in the opposite direction. BUT it is not obvious that there is a pin or tab at B in slot B. Slot A can snap into place under the edge of the housing at E. Or the door can be used in several models and the locks on A and B CANNOT be used.
A lock that is used is in
C with the current locomotive tab at D. This works with the Bendt-Lock arm at H. The arm at G with its shape indicated by a vent line is inserted into the space at C, and the Tipo slides under D when the The door is pushed into the locked position.
It is not obvious what happened in your case, but if this were my camera, I would consider the following.
Hold the camera down with your right hand and hit the top sharply with your left hand so that a muffled but solid impact occurs. Repeat several times. This has the effect of driving the batteries into the body and possibly removing an obstacle.
At H, insert a thin, stiff metal object along the line of the purple arrow. A nail file or a piece of spring steel (as used in some large wooden boxes as strapping when shipping). The goal is to work between door and hook at H and try to release the sliding effect of the lock.
Try to pry with a thin metal object between the body and the door (outside on the body side of A) to move the door in the unlocking direction. Tapping the camera gently but firmly during the experiment can help.
Use a drill with a diameter of approx. 6 mm (Really!) To drill into the door on the outside next to point D so that you can see and access the top of lock H WITHOUT DAMAGING IT. Once you are ONLY through the outside wall of the door, you can use a hand-held reamer or a larger drill (10 mm) to enlarge the hole without damaging the hook at H. This way you can determine if the hook is jammed. You can cut the edge around hook H without damaging H. IF this is the only lock, the door can be opened or partially opened without sliding.
You can also use this hole at the edge of the hole to apply more force in the direction of being pushed open. As long as you don't damage hook G, everything you eat for dinner is marked on the door. The hole can be filled easily.
Alsop, doors can be cheaply available on a used camera or as a spare part. If you attack the door gradually, you can open it at the appropriate time. If the actual camera is undamaged, it should be possible to install a new door after the problem has been identified and resolved if it is in the body.
Note that the two plastic bars at D should prevent the battery from being inserted with the opposite polarity. If someone succeeds in closing the door with a battery with the wrong polarity, it puts immense pressure on the door – it may only take a lot of force to push the door.
It is not obvious that the white material near G should have any effect. But I can be wrong.
See picture below.
added: Despite the counter option of the phantom downvoter, the above information can be helpful when opening
If I had your additional information about the lock button, I would try to insert lever objects (e.g. screwdriver tips) into the areas around the pinched button and apply extra force in the desired direction.