I posted too soon. The battery charged only briefly, and is now resisting a recharge altogether, including via the aforementioned utilities. However, the machine recognizes its presence and EMMpathy will report accurately about it (e.g., 0% charge). I think I'll leave it plugged in for a few days and see what transpires, and still suspect the dead backup battery might be the source of the trouble, but wonder if a transplant of a spare logic board I have lying around would be a good idea.... The spare was known to work a couple of years ago — came out of a machine that basically fell to bits and so had to be disassembled for parts.

A basic problem is that the machine seems every few minutes not to recognize that it is plugged in - which means I get a "plug in your adapter" message. But the behaviour is also changing, even if it is erratic; it used to shut down randomly, now it goes to sleep briefly after a low power warning.

I reckon that the trouble's the power manager/backup battery. i know from experience that this can cause all sorts of odd behaviour on other powerbooks of my acquaintance. However, maybe the changes are good, an indication that something is getting juice that was not before: we'll see.