Restoring doesn't work anymore, iPhone won't start/charge

Trying to keep the story short:

My iPhone5 shut down because of an empty battery. I tried to charge it after 6 hours but it just started rebooting over and over (blinking apple startscreen).

I tried all recovery modes, I talked to apple care for 2 hours, installed iTunes new. tried every possible thing like checking hosts, firewall...

iTunes reacts to my phone (but it doesn't show my iPhone data on the side anymore just n/a) when I want to restore it starts but suddenly it diconnects the iphone and shows error 21.

I'm totally lost, apple store couldn't help either.

I bought the phone in Nov '12, got a new device in July '13 (because home button was broken), and nobody feels responsible now.

I paid a lot of money for this phone and I didn't do anything wrong.

Is there any chance people have experiences with this, maybe a battery change?

It's very sad apple says they won't replace eventhough it's obviously a well known problem that iPhones have hardware problems since ios 7.

maybe someone can give me an advice.

thanks!