2 days later....the solution seems to be to just keep it going & not plugged in til the battery empties (backing important stuff up meanwhile). From the fact that it took several days, I gather the "battery 0" warning is part of the misfunction. During this time you can sleep it manually w the "power off" control on the charms bar, being careful not to turn it off (cos then you wont know if the battery's emptied yet), and turn it on w the home key.
Once the battery is totally empty (no reponse of home key, little blue light by power button off), you plug it in and it works.
My guess is this explains what happened previously when I (& others I read) sent it for repair. By the time it got to the workshop the battery had emptied, so they plugged it in, found it worked, & returned it with a message like "you must have forgotten to charge it", missing the problem.
We'll see: if it's something that happens every few months, & is this easily solveable, it's not so bad. Particularly since one can still use it while waiting for the battery to empty.
Wonder if regularly letting the battery get to empty ever few months would prevent the phenomenon?
Be interested to hear what others found.
Rivka