Taking/Extracting a Stucked Battery Out of a Nikon Coolpix P510
1st off, pull the yellow tab to allow the battery to be pushed out.
-with the use/aid of a thin metal/sturdy objects like a knife and long-nose-plier; carefully/gently wiggle the stucked battery upward/outward of the camera's battery compartment until it's exposed enough to pull it out with the plier.
Once pulled out/extracted; carefully examine the battery and the battery compartment and the springs that made it pop out whenever you replaced the battery. If there's corrossion/rust; clean the corrossion with Q-tips and rubbing alcohol; and dry them before replacing the battery with a new clean one.
The main causality of this is a swollen Lithium Ion batteries. Be careful though not to puncture them because they might explode.
This procedure will hopefully work with other cameras with Li-Ion battery packs.