De-solder the existing soldered connections and remove the speaker from the rest of the device.

Insert and solder in a working speaker of the same model. Make sure the points where the wire ends connected are consistent with the old speakers.

Note: If you notice that a wire is disconnected, this may be the cause of your problems. Re-solder the connection to fix it.

You can refer to iFixit's guide or this informative video for more information on soldering.