There is another unexpected behavior that I forgot to mention.
If I turn on the laptop with the battery plugged, in the power management preferences, there are three tabs: On AC Power; On Battery Power; and General.
However, if I turn on the laptop without the battery attached, I can only see two tabs: On AC Power and General.
This is not completely absurd.
But, if I plug the battery with the computer on, it still show only the two tabs: On AC Power and General. And even if I then unplug the AC power and use only the battery power, I continue to see only the same two tabs in the power management preferences.
I don't know if this is related with the problem reported or if it is a new and independent problem.