Got it working. Thanks for the "check the obvious" tips, I must have just had the sound way way down, and only turned it up a little bit the first time I tried.
The speaker kind of sucks, so I'm sure I'll want to "upgrade" at some point.
OK, something is definitely wrong. It sounded like half of the sound effects were playing, and then there was a burning smell after a minute or so.
I turned the machine off, and the smell was still going. It turns out it is coming from my laptop, so that's an entirely unrelated issue, apparently. Still, I was really worried about the cabinet.
The sound is all weird, though. I don't know how to describe it, it's like it is playing static for half of the sound effects.
The static for half the sounds only happens in World Heroes 2 Jet. In all the other games, it's like for every sound effect, the volume is the opposite. So what is normally loud is quiet, and vice versa. So I'm getting really loud back beats of music, while most sound effects are really quiet.
I uploaded a video to youtube (well, I'm trying to, hopefully it will be up soon) :
http://www.youtube.com/watch?v=tWnLqQQLA0w
Another video
http://www.youtube.com/watch?v=URXIuQVEbRE
kernow helped me out in chat. it sounds like I need a JAMMA to MVS converter board, whoever converted this cabinet did not finish the wiring or something.
I think I need to order this?
http://www.jammaboards.com/store/neogeo-mvs-to-jamma-adapter/prod_198.html
Also, I think the burning smell is just the fireplace. I live in an apartment, so maybe the guy above me is using his?
I put in my 1-slot board to test, and the sound is perfect. I'm going to order that converter