Sonicare brush doesn't work even though lights are on.

Yes - Inside the sealed case is a glued & soldered & welded you-can't-get-me-out Li-on battery.

How old is it ? Mine is old and has become "brush-as-fast-as-you-can".

If you can get it apart, yes, you could replace the battery. However, most of them wear out & leak where the gear shaft meets the brush. If yours is the charge-by-wire type, I advise users to store it BRUSH DOWN, to avoid leakage. If it is the charging-stand type, always give it a vigorous shaking after each use.

I'd wait for Santa to bring a new one ;>)