check your wiring going to the main PCB cage, make sure no connectors are halfway sticking out or anything.
then, look for the sound board, it's the one that's got like RCA audio jacks on it, make sure all those connections are good.
then follow the RCA wires to the amplifier boards, I think there's 1 or 2, I get this one and Daytona 2 mixed up, make sure all connections are good there too.
I think it's commonplace for if the speakers are blown, it can blow out the ICs on the amp boards, and that might contribute to the problem you have.
it's very easy to plug the connectors going to the main board in wrong as well, there's no seat speakers on this game like Daytona 2 though, you really shouldn't have any problems with the engine sounds overpowering the music on this one UNLESS you have another potential problem..
if you have a sitdown unit (you didn't specify, so I don't know

) it's very easy for dirt and crud to form on the various boards underneath, and I actually broke a ROM socket on a sound board trying to press the ROMs on the sound board down (it forced some like wood chip fragments or something in the socket) and I had to go through a major ordeal to replace it, but I fixed it.
if any of your sound ROMs did some "chip creep" it could contribute to this, best way to make sure is to go in the Sound Test and play EVERY sound sample and song and if any of them come out sounding garbled or don't play at all, it's more than likely a ROM issue.
if that's the case, PM me, I can help you try some other things.
my family operates a game room with a Daytona Twin, and I've done my share of maintenance and cleaning to keep that thing running and to de-rig what the assholes that had the game before us did to it.