iPhone won't switch on - will Apple replace it?

My iPhone 3G won't switch on. I left it in its dock next to my bed on Tuesday night and woke up late Wednesday morning because the alarm hadn't gone off. My iPhone was dead. Not even the 'connect me to a power source' screen.

Tried holding the home button and lock button together, tried connecting to iTunes, tried DFU mode. Nothing - it's totally dead.

I went to the Genius Bar on Tuesday but their appointments were fully booked until Friday. The lady looked down the headphone jack and told me to come back Friday. I googled what she was up to and looked in there myself with a torch - no pink so it's not water damaged.

My question really is will they replace it? I got my 3G on launch day as an upgrade from the original, but that had to be replaced because the screen died. They swapped it in store no problem. I can't remember but I think it was less than 12 months ago.

Is the phone only covered by warranty for 12 months; and if so; since I have a replacement, does the warranty re-start from the day I got the replacement?

I have insurance so could always claim on that - but any advice would be appreciated. I will let you know how I get on tomorrow.