Are you able to test the charger? does the light come on when you plug it in
As far as the sticking keys here is a good video to watch on how to remove the keys. I would use a lens wipe to wipe the key and the area down before assembling. I show students all the time how to clean their keys.
Bonus video
I would use an L shaped pick like this to remove the keys because it will do less damage to the rubber nub in the middle. Once the nub is damaged and will not stay on the keyboard is damaged.
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