From your description it sounds like you may have broken off the volume slider located inside the console. This slider is soldered onto the motherboard. If it was just the external slider that was broken then it would still have sound, it would just be stuck in one place and you wouldn't be able to adjust it.
This is most likely not easily fixable. If the slider broke off it probably tore off circuit traces on the motherboard, which would be very difficult if not impossible to fix.
The best fix would probably be to replace the motherboard.
I hope this helps.