Hi and welcome back to JustAnswer,Thank you for the question and your patience. Should you still need assistance for information purposes only...Initially, a little more background info please:
Appreciate the additional information.
Have you tried cleaning the battery terminals and the camera's battery contacts?
Cleaning is the only easy user doable attempt.
Could you try having the battery tested with the use of a volt/multi-meter?
Checking the battery with the multi-meter would confirm if the battery is able to charge to 3.7V and if capable of delivering the 1400mAh. Other than a test, it would also serve as a process of elimination. If the battery checks good, then it would be an internal hardware issue with the Nikon COOLPIX P520.
The alternative is to replace the battery which then would serve as an attempt of a fix and as a test likewise by process of elimination.
Please post back how you would want to approach this and/or should additional information be needed.
Yes please, test the battery.
...or if even with a new/fully charged and known to be good the battery problem persists, then it would confirm the internal hardware issue with the COOLPIX P520.
Good luck and thank you too for the opportunity to be able to share the information.