The Chromebox in question was found in an e-waste bin with a sticky on it reading Dead. I don't believe such pronouncements unless I can verify it for myself.
It requires an external 19V power supply. I didn't have one on hand so put the box aside until I could lay my hands on one.
A few months passed, then I found an HP laptop power supply in the aforementioned bin. Time to power up the box.
It turned out that the barrel connector is not the right one. The Chromebox wants a 5.5 mm external diameter, 2.5 mm intenal diameter connector. The HP connector is 2.1 mm internal.
I can get a power supply for about $10 delivered. But I'm loath to spend money unless I have some assurance that the box works. I found that if I held the plug against the socket I could maintain the supply. So held the connector in place with a rubber band, connected up a HDMI display and pressed the power button. I got the OS is missing message similar to the second screenshot in this Lifewire article.
Well that's good, the CPU is working, and probably the RAM, but maybe the SSD isn't.