The 'takedown pin' is the slide stop, you guys. Like a 1911.
You cannot remove it unless you withdraw the slide far enough back.
Just like a 1911.
Primitive as it sounds, a common method with these pistols
is to hold the slide firmly in your left hand,
and hit the back of the grip HARD with your right hand.
Repeat.
The idea is to hold the slide still and move the frame forward,
rather than pull the slide backward. The physics is the same.
You just get a better grip on it that way.
If broken parts are jamming it up, no expedient method will work.
If you're worried about damaging your gun, just take it to a gunsmith.
The pistol is worth proper handling and repair.