If the IHF (integrated hands free) speaker seems just okay but still there no sounds can be heard on it when playing a music or ringing tones, you may then proceed to trace and check all the corresponding components that holds or connected to the IHF speaker.
This solution below will help you locate those particular components location where it is being mounted on Nokia C3 PCB board layout.
Nokia C3 Ringer, Hands Free Speaker No Sounds Solution
Those components showed on the solution above is located or being mounted on the right side of the shielding metal. Just check all these components and just replaced if found faulty or damaged.
The filter coils near the IHF speaker pins contact pads may oftentimes causes the problem, if these filter coils open or being cut-off due to an audio signal overdrive. Some factors are caused by oxidation build up if the device suffered wet or water damaged and any means of liquid.
Replacing and cleaning certain components that seems to be faulty or being damaged might possibly fix Nokia C3 ringer and hands free speaker no sound output problem.