The sound hardware on the Durango/Vegas boards is essentially the same as the old stuff developed back in the MK2 days. The difference is that, instead of storing the sound effects in ROM chips, they're stored on the main program hard drive and loaded into a DRAM by the game at runtime. This means that, if that DRAM is bad, the sound system is effectively unusable.
The startup process should visually identify the location of the bad chip. If it doesn't, take a picture of your boardset, and I'll point it out for you. It's on the IO PCB (the one with the JAMMA connector).
Check for cracked solder joints on the bad chip. Otherwise, just replace it. You may be able to get a suitable chip from an old PC SIMM (I think it's an EDO or FP type). Failing that, you'll probably need a donor dead Durango/Vegas or maybe Seattle board to steal one from.
(Durango and Vegas are very similar - I don't remember which one Blitz/Showtime uses)