Has it been left discharged for a significant period?
In any case I think it will need a new battery, it's sort of do-able at home if you can deal with tiny screws and probably detaching a ribbon cable inside for access. I would try opening it and check battery connections are good first, and go from there.
There will be some useful tutorial on youtube about opening it as they do it a lot to add boosters etc.
You might find a used controller on ebay or something would would be easier.