PC Speaker weirdnesses

Today we were trying to do some debugging by getting some tones out of a laptop speaker by frobbing bit 1 of port 0x61 on the keyboard controller.  Rather unexpectedly I got no sound whatsoever out of the speaker, yet I had managed to do so the day before.   So I double checked what had changed since the day before:

1. Was it because I upgraded my kernel?
2. Did I unexpected disabled the speaker when tweaking BIOS settings?
3. Was it something interfering with my port 0x61 bit twiddling?
4. Was the hardware now broken?

As per usual, I first assumed that the most complex parts of the system were to blame as they normally can go wrong in the most subtle way.  After a lot of fiddling around I discovered that the PC speaker only worked when I plugged the AC power into the laptop.  Now that wasn't obvious.

I suspect I should have applied Occam's Razor to this problem to begin with. We live and learn...