My iPhone won't power on, even after 2 trips to Apple repair service.

My iPhone5 won't power on, even after 2 trips to Apple repair service. I got it back both times with the invoice stating "Battery replacement kit". Now an Apple customer service agent (Sean Greaves) says they won't replace it because it "supposedly" worked when they had it, and he won't respond to my emails. I have tried everything Apple has told me to, and it still won't power on - can't even get the battery symbol to appear. All I want is a replacement since this is the second time it came back not working,and they won't live up to my Apple Care Warranty.