Are you able to test the charger? does the light come on when you plug it in
As far as the sticking keys [https://www.youtube.com/watch?v=Kl--uszqAq8|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.
[https://www.youtube.com/watch?v=pY7wNiA5ow8|Bonus video]
I would use an L shaped pick like [https://www.amazon.com/TEKTON-6943-Precision-Pick-4-Piece/dp/B000NPPBQK|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.