just some thoughts to stimulate your diagnosis..
I never thought of it this way, what would happen if you ran it WITHOUT the ribbon cable, would it still just play the BONG! sound on power up?
if you say you resoldered a chip on the heatsink, that's the amplifier. obviously wouldn't hear anything if that wasn't working. okay.. the wiring harness that goes between the main board and sound boards is the one that carries power to the sound board (+5, +12, -5 and grounds) and it has the blue and violet wires if I recall, those connect to the speaker output at the JAMMA harness.
the ribbon cable will connect to headers on the main and sound boards, and both headers will have numbers on the pins like 1/20 and 19/20. very easy if you're not paying attention to confuse the 19/20 as a 1/20 based on what I've seen in past threads here. the red striped edge of the ribbon cable needs to be aligned with the 1/20 on both sides. verify this first (with the power off if you do need to flip it around). then go into Test mode, go under Diagnostics and then Sound Board Test. if it says something like "SOUND IRQ NOT DETECTED" then you don't have signal between the main board and sound board. if it says "SOUND IRQ OK" then you should have working sound.
now another thing that you could check, based on personal experience... is the game roms on the main board located at UG12 and UJ12. my game was sold to me as working, and it would work, until the one time it wouldn't and all I heard was the Wasteland music and baby crying sounds. even though all my connections were good, I was still getting the "SOUND IRQ NOT DETECTED" error, despite the game playing sounds, albeit, wrong sounds. when I pulled the UG12 and UJ12 roms I found 2 chips that were plastered in corrosion. Broodwich and I will then famously say.. get the fine grit sandpaper out and start grinding that crud off.
beyond that, I'm going to say it's a good sign you're getting the BONG! sound on power up. means your amplifier works, your speaker wiring output works and... your sound board for the most works I'm guessing. start by checking the ribbon cable. if you want to swap another in, you can use a computer IDE cable, even one that has a key in it, because one half of it will have 20 pins. if no key though, and your cable doesn't have a red stripe or equivalent, just draw along that edge with a sharpie and consider that your pin 1/2 side and connect it accordingly.
hope this all helps.