... and that did the trick, or I should say that Intelligent Battery Recondition did the trick. Emmpathy had gotten the battery recognized, but seemingly could not get it into such a state as to enable recharging. IBR did the "pre-charge" repeatedly over 10 mins or so, and I now have a lightning bolt and one bar and counting in the Control Strip.

One further query: hitherto the machine would shut down after 10-15 mins if put to sleep. A known backup battery anomaly, perchance, or buggered power-related hardware? Go on, give me something else to celebrate!