Hi Dashmellow, thanks for your reply. It works fine on the battery (it's running on my desk right now). I can't see any flaws on the mini-USB connector (this inspection required a comedy combination of glasses, jeweller's loupe and a torch held in my mouth...). Was your USB flaw visible from the outside, or did you open up the camera? I just opened up the camera for the first time (didn't want to earlier, from worrying about any warranty from the supplier) but don't see anything out of the ordinary.
It's the way it refuses the first start of the day that really baffles me. Once you've persuaded it into life, subsequent auto-starts seem pretty reliable. That's behaviour I'd expect from something mechanical, not electronic...