That's a generic small MP3 player, probably with a 3.5mm headphone jack, right? I think the most probable failure would be a broken solder joint between the PCB and the jack, caused by mechanical stress on the plug. Have you inspected these joints carefully, with a magnifier? Or just try to carefully re-solder them.
If it is really the amplifier chip that is broken, would you have a chance to repair it? (Can you desolder and solder these SMD parts? Is it an amplifier chip that is readily available, or some exotic single-chip solution for the whole player?) If the answer is "no", I would not bother beyond checking the output jack and its solder joints.