One of my nanoKenbak-1s had been running the clock overnight on the bench. I needed to temporarily use the power cord this afternoon for something else, so switched it off and pulled the cord. Later, when I switched it on, it went through the power up animation but none of the 15 buttons worked except for BIT 3, which toggled the LED for BIT 0!
Looking at the schematic, it would seem that that symptom implies that the 16 bit shift register was not shifting. It is clocked by pin 17 of the ATmega328. Using a multimeter, I found some non-zero signal on pin 17, but not on pin 2 of the two shift register chips. A continuity check showed that there was no connection 17 to 2. I pressed down hard on pin 17 with my fingernail, switched it on, and the buttons were working; let go and they stopped working.
Fix: a touch of solder on ATmega328 pin 17. Being an end pin, it was fairly easy. Don't know why that pin just decided to randomly let go, but I decided I'm not a fan of SMT.