it sounds like (no pun intended!) the audio pre-amp has been damaged. This is an IC that acts as a buffer between the CPU and the external world. Since the sound quality is poor for all options, it suggests that the sound source (pre-amp) is at fault. Yes this can be replaced, but someone with knowledge of its location and the skills to replace it are required. Your best bet is to visit an Apple store or to get the unit to someone capable of micro-soldering that knows the MAC mini product line.
Dan