Spent part of the day cleaning Command Central. Part of the cleaning involved untangling the nest of mini-headphones from various manufacturers that I have. And since I still had the little sound system connected up to the computer and it has a headphone jack, I figured I'd plug in a set of headphones and see if that worked. And it did-- it would mean I'd have to wear headphones, but I could continue working.
Eventually I got to the point of disconnecting the sound system. I unplugged the headphones.
And there was sound. It started working again.
It cut out briefly a few times in the interim. I suspect that there's a relay on the mainboard that's either going bad or the driver for it is getting weak.
Still, for now it works and it's staying on through power cycles, so I'm just gonna leave it alone for now.