I'd start by using MAME to help figure out where in Spy Hunter's complex audio hardware the machine gun sound is generated. A few minutes of playing shows us that it's generated on the SSIO board, by one of the AY-3-8910s (the one MAME calls "ssio.1"). Specifically, channel 0 of the 8910.
Then I'd go to the schematics of the SSIO board, and check out the 8910's and what's down-stream of them (before the channels are mixed together).
You might start by swapping the AY-3-8910s and seeing if that changes your situation or not. If it does, one is bad. If not, the problem is down stream (perhaps in the 4016/4066 switch, or the op-amp).
Or, of course, it could be due to some physical damage on the PCB, or a shorted component, etc. But armed with the schems and knowledge of where the missing sound comes from, you can focus your search.