iPhone 5 dead, but... Apple Phone Support sorted!
My phone was at 30% when I plugged it in last night, and when i plugged it in, it made the charging sound and showed the battery icon as per normal. When I woke up this morning it was dead. I tried it on a different socket, tried the Lightning cable in the USB port, still nothing. I was convinced it was a lignting cable issue, as others have reported. I filled in the Apple Support request for a "call me now" clicked next and my phone rang! I'm talking within a second or so at the most. I spoke to a very nice lady who asked me to try a reset (hold in both buttons for 20 seconds) "yeah, like that is going to bring it back to life". Anyway, up pops the Apple logo and my phone shows fully charged. So no idea why my phone had died over night, as it was fully charged, but just being put down to a 1 off glitch for now. Very impressed with the response of Apple support, which save me a trip to my nearest Apple store.
Great outcome.
iPhone 5, iOS 6