I know for a fact that the ACH(X) boards are some of the worst made. They were manufactured in China and are prone to a lot of issues. I had one myself so I know first hand. Can you post some pictures of the socketed chip and the bypass? I know there are flex patches for the NEO BUF floating around somewhere and I would definitely replace and wiring job with one of those if you have the capacity to do so. I'd also head over to the NeoGeo Dev Wiki and find out what chips are related to audio processing (start with the z80 page it references NEO-D0 and NEO-C1) and see if you can find any shorts, damaged traces or vias, or corrosion. Also take a look at the cartridge connector pins because audio issues can arise from a dirty slot. If you haven't already, clean the cartridge slot and the games pins -Plenty of tutorials online for this- NO BRASSO. Also clear the backup ram and see if any of that helps. You can clear the ram by either flipping all the dips on and powering the board and it will say work ram test or the like, leave it for a minute and then power off and reset the dips. Other wise go to the hardware test screen and flip through till it says press A+B+C to clear back up ram. Lastly, how is this board powered? Is it in a cabinet or supergun? Is it 5v modded or the original 12v mono?
Like I said, some pictures will help immensely, try to get clear bright shots on something that can do higher resolutions and upload a photo set to imgur. I will be more than happy to help you get this thing working.
Cheers!