Well I'll be ........
After posting my question, I spent some more time digging around for suggestions. I found a thread where someone had fixed the same problem (different Toshiba) with a BIOS update.
Nothing to lose so I tried it and bingo, the battery is back! Even more surprisingly, I didn't mention earlier that the battery wouldn't charge when the machine was shut down. It does now! How on earth a BIOS update can fix that is beyond me, but, it's sorted!