Thesandlord: No, I've been storing most of my files (but possibly not all, which is why I'd like to recover rather than reflash if possible) on SD cards, but booting from internal memory.

tgalati4: the current battery is only a couple of months old - I replaced it earlier this year because the original one was giving me rather crummy amounts of runtime. I've tried the old battery (which I'd not had any booting problems with) too - no difference.

Thanks anyway!