I drained my battery yesterday and it wouldn't charge anymore too. It didn't even recognize the chargers (Apple original USB Lightning cable, Lightning cable with power adapter, MicroUSB-to-Lightning adapter and certified car charger) and when I pushed the power button on the device, the screen popped up that a cable needed to be inserted in order to charge it, even though the cable was in.
I've tried everything... A different cable, different computer, different power outlet, different MicroUSB cable. Every single option I've tried, but without success.
Then I decided this was a problem for Apple to solve, so I created a repair request on their website. It said that I should not send the accessories and take out the SIM-card. And miraculously the phone started charging after I got out the SIM-card! Still no luck with the MicroUSB-to-Lightning adapter, but the cable and the power adapter seem to work now. Even after putting the SIM-card back in.
Strange... :-S It looks like it's charging now and I will let you know if it came back to life later.