nah the cases are plastic as far as I know. a hard plastic, but still plastic. wow AD8397 and looks like a bypassed buffer.OK well sorry distracted there lol. OK well the ground terminal is the one closest to the panel edge, where you have broken it. I would say the central grounding point (star ground) is at the ground wire of the first power supply cap or the ground of the charger input. you could test for continuity between those points. but by the look of your damage there, your problem is that when you ripped it out and broke that piece off, you destroyed the part that was holding the ground ring in place.
I can see that the ground terminal seems to be further out/looser than the other jack, you could try just bending it back in so it causes better contact. do this while the case is open and music is playing, just take care not to short anything. otherwise you could find out what type of jack it is and replace it. also if there isnt contact to ground from that terminal, you could even do a quick and nasty fix/test, by connecting a wire from the input jack ground to the output jack ground, they are probably one in the same anyway. my guess its more a mechanical connection issue rather than an electrical connection issue. most likely even when you think you are getting a good connection, its slightly marginal because of the ground ring not being held firmly in place, allowing the radio frequency to sneak into the ground. or its just been there all along; as by the sounds of it you have to have the amp up way louder than you use it to hear it. since its quite a low power amp and with a plastic case, it wouldnt be that hard for noise to be coupled into the signal
hope that helps