Every time my Nokia Lumia has automatically shut down it has been because it's battery was critically low. My fault for not spotting it!
However, occasionally, the phone has been impossible to switch back on - even though I thought it had been charged via a (UK) 13A socket charger for over 6 hours.
The solution is to plug the phone into your PC via USB instead. It only took about 5 minutes of charge via USB before the phone woke itself up. The display then told me the phone battery was 'critically low'. At this point I was able to substitute the USB lead with the Nokia charger. This time, the red 'charging' light came on continuously; the phone stayed on, and the display reverted to normal, showing time and the battery charging symbol.
Reason: if the battery is very flat it demands more current than the 13A charger is designed to provide, indeed it is protected from supplying it to stop it damaging itself (can see the light on the charger flickering between red - charging, and green - implying 'charged' as it struggles to provide the current.) At the same time as the charger light flashes, the Windows logo on the phone flashes, in sync with the 13A charger. The PC appears to be able to deliver enough current to start the charging process, and once the battery has enough small charge, the 13A charger will work.
No factory reset needed - just enough current to get the battery charging again.
