I guess I should add this here so it has a chance to get voted up as an answer:
After replacing the AMP-NUS with a known-good spare and replacing every capacitor between it and the AV multi-out, I still had no audio. I was measuring voltage on pin 1 of the AMP-NUS when my probe slipped and momentarily shorted 12v from pin 1 into pin 2, instantly restoring audio. AMP-NUS pin 2 goes to ground through C28… nowhere else. Because the AMP-NUS was already replaced with a known-good spare, that means C28 is our culprit.
I never finished installing my replacement capacitor kit. I wanted to see if audio failed again so that I could see if replacing C28 also works but it’s been 2.5 years and it’s still working great. I haven’t come across any more with faulty audio to try replacing C28 but StealUrKill above replicated my results. He restored his audio by deliberately shorting 12v to C28.
My hunch is that faulty mainboard capacitors only happen on very late model N64 consoles as the industry was reformulating capacitors for RoHS compliance and the formulas weren’t yet refined. Mine was a NUS-CPU-09-1 revision board (the very last) inside a NUS-101 “Pikachu” console and I saw another with a capacitor-related video problem which was also a Pikachu console. My C28 is a 25v Panasonic/Matsushita HA series electrolytic with no “lead free” dot but this was well after manufacturers began reformulating (see “the Capacitor Plague”).
TL;DR: Power on without the heatsink and momentarily touch pins 1 and 2 of the AMP-NUS together with audio playing. You’re welcome. ;)