There is a golden rule of electronic fault finding. "Thou shalt always check test thy voltages".
Check that the new battery works with a multimeter, then check the battery contacts to see if they are clean and corrosion free, then check the movement to see where the battery contacts route to on the circuit board, and using the multimeter again, check to see if the voltage actually appears on the circuit board.
Often movements will have test pads (little exposed, often round pads) specifically for checking the voltage, (and sometimes other things, like the oscillator).
Start with this, since if you have no power, then no amount of "fiddling with the gearbox" is going to get things moving.
If the battery is good, and the oscillator "oscills" then move on to the mechanical side.