Just an update on this issue (in case anyone asks about something similar in the future)...
The DOA TB47 has been sitting in the case since that fateful first day, but on a whim I decided to plug it back into the charger this morning. Before doing so, I held the power button down to check the current charge (which, on Saturday, did absolutely nothing). TODAY, however, the first green light came on. I plugged it into the charger, and it seems to be charging now.
I don't know with any certainty why it was completely unresponsive on Saturday, but if I had to guess... it might have been too cold. When handling the battery, it didn't feel cold (cool, but not cold), but it had just been delivered by UPS at about 8:30AM. In Denver. For all I know, it had been sitting in an unheated truck for 12 hours previously (and we'd just gotten snow the day before, so it was chilly outside).
I'll keep an eye on it to make sure the charge completes, then update its firmware. It would be so lovely if it turns out to be a working battery, even if it means I didn't need to buy the TB48 on Saturday afternoon. I'd have gotten an extra battery eventually, it was just a tough pill to swallow after laying out the money for the Inspire itself. Still, all's well that ends well.