If after replacing the battery the Fitbit still doesn’t work (except when connected to the charging cable) check the supply fuse (markedF1) just below the red square in the above picture next to to the red battery lead pcb connection. The fuse may have blown when your old battery went short circuit.

I temporarily jumpered it out after replacing the battery and the Fitbit now works :-)

Unfortunately I have no information as to the current rating of this fuse?

If you know please add this info for me and others to benefit :-)