Rushing - more later if it looks like it may be useful:
I do not have any experience of this particular camra.
But, working on general principles.
Slots at A and B are locking slots.
A pin enters the slot when the door is closed and then moves into locking position under the overhand when the door is moved sideways.
The red arrows at A show the path that the body lopcated locking pin would take to unlock. The door moves in the opposite direction. BUT it is not obvious that tere IS a pin or tab at B that works on slot B. Slot A may lock under the body edge at E. Or the door may be used in several models and the locks at A and B MAY not be used.
A lock that IS used is at
C with the actual lok tab at D. This works with the bendt lock arm at H. The arm at G with its shape shown by a vent line is inserted into the space at C and the tipo slides under D when the door is slid into lock position.
It is not obvious what has happened in your case but if this was my camera I would consider doing the following.
Hold camera upside down in right hand and strike the top sharply on my left hand so there is a cushioned but solid impact. Repeat a number of times. This has the effect of driving the batteries into the body and MAY clear an obstruction.
Insert a thin stiff metal object at H along the line of the purple arrow. A nail file or piece of still thing spring steel (such as is used on some large wooden boxes as strapping when shipping). The object is to workl bewteen door and hook at H and try to free up the lock sliding action.
Try levering with a thin metal object between body and door (on outside on body side of A) to try to get the door to move in unlock direction. Tapping the camera kindly but firmly while trying this may help.
With a dril of about 6 mm diameter drill (Really!) into the door at the outside next to point D so that you can see and access the tip of lock H WITHOUT DAMAGING IT. Once you are JUST through the outer wall of the door you can use a hand held reamer or larger drill (10mm - up to enlarge the hole without damaging the hook at H. This allows you to see if the hook is jammed. Better, if you can cut the ledge away around hook H without damaging H then IF this is the only latch it may allow the door to be opened or partially opened wothout sliding.
Also, this hole allows you to addply more force in the sliding open direction using the edge of the hole. As long as you do not damage hook G then all you have dine is marked the door. The hole can be filled easily.
Alsop, doors may be available cheaply on a used camera or as a spare part. By attacking the door in stages you WILL be able to open it in due course and if the camera proper is undamaged it should allow a new door to be fitted after the problem is determined and fixed if it is in the body.
Note that the two plastic ridges at D are intended to stop reverse polarity battery insertion. If somebody managed to shut the door with the wrong polarity battery there it would insert an immense pressure on the door - perhaps only much force is required to slide the door.
It is not obvious that the white material near G should have any effect. But, I may be wrong.
See picture below.
Added: Despite the phantom downvoter's option au contraire, the above information may help with opening
Given your extra information about the locking button, if it was mine, I would try inserting levering objects (such as screwdriver tips) into the areas around the jammed button and try exerting extra force on it in the desired direction.