This fixed my problem! Thank you so much. I plugged my Cayin C9 into a laptop USB port, which has never caused problems before, and it apparently entered protection mode. The power light would blink several times, and the battery-level indicator lights would light up, showing all four lit up; but then the power light would turn off and the amp would never start. Charging overnight from a wall wart got it working again. I love this amp, and it's expensive even on sale, so I'm so happy it's working again. (I've thrown away the USB cable, just in case it's a danger to electronics.
One last thing: could a static discharge from my finger trigger protection mode?