iPhone 5 won't charge

Yesterday I plugged in my iPhone 5 32GB to charge and noticed the battery symbol turned to a 'plug' icon as opposed to a 'lightning bolt' icon. The phone was on 18%, so it should have been a lightning bolt. If I'm correct the plug icon should only appear when the phone is fully charged. Anyway, it stayed with the plug icon for a bit, refusing to charge up and after 10-15 minutes and trying a different wall socket the lightning bolt suddenly appeared. Sure enough it charged all the way up to 100%.

Today is another story. I've been trying all day to charge and nothing will happen. Phone is now completely dead. When I plug it in the 'dead battery screen' appears (empty battery with a little bit of red in it, lightning bolt underneath) but it never actually charges up and turns on. Its been like that since this morning. Been into my local Vodafone store today, left it with them and tried another charger, no luck. Tried hard resets, no luck. Vodafone are sending me a replacement handset for Tuesday, although Saturday to Tuesday with absolutely no phone is going to cause a fair few problems. Apple can't offer me anything any faster - all London Apple Store Genius bar appointments are fully booked until 19th October(!). I've just managed to get it into recovery mode in iTunes and am trying a factory reset right now, but don't have high hopes.

I've searched the web a lot and not found any similar stories to this one. I've more or less accepted that I'm going to have to wait until Tuesday now, but thought I'd post anyway to make sure people are aware of this particular series of events and in case anyone is also searching to answers for a phone with simlar symptoms.

Any ideas are of course welcome, although I believe they've all been tried!