Lets backup here... Did you smell something burnt? Do you see something damaged?
I can't locate the capacitor labeled C3833 the highest listed is C3387 within the schematics and board views for your system. So, you really need to aim us to the the component which you believe is damaged so we can identify it.
Also, you posted two images of the backside of the logic board, how about the other side? The resolution is not good enough to see much.
Given the age of the system I'm more inclined to believe the battery has failed vs something within the logic board.
The other possibility given your charger never getting the battery charged (stuck on Amber) after letting it charge for a good eight hours. Your SMC comparator logic is damaged from using a knockoff charger. What I often see is the small resistors burn out.
@Julian - Bingo! Chris @imicrosoldering was able to decipher what you where aiming for. Great work Chris!
To finish the answer here is the caps identifier: C7376 as you can see in the boardview
Your zoomed in image helped in finding the needed tree in the forest!
Here’s the schematic view
Which is how Chris ID’d the capacitors values.
Now the hard part! You’ll want to practice your soldering skills before you attempt to replace this cap your self. There is a bit of art involved in micro-soldering. Maybe you should locate someone who has the needed tools and skills and have them do it.
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