If memory serves me correctly, the AIO simply does not have a power button. There's a power switch but power control is all done via software and ADB. Standard disclaimer: I haven't actually touched one of these for 16 years but there were a few similarly afflicted Macs over the years.
Definitely bring your ADB keyboard (a known working one is preferable ;) and use the power button on that to start the machine. If the machine doesn't respond then maybe you have a dead PRAM battery, loose connectors, dying capacitors on the motherboard or PSU, ...
Also, try the CUDA reset button on the motherboard.
I am hoping it's just the lack of proper keyboard. I have 3 good ADB ones that I use often, so I'll be set there. I think I'm going to try to talk him into letting me open the back. Looking online, the AIO's look real easy to open.
I'll have to look up the board diagram for the CUDA button too.