My iPhone 5 refuses to turn on?

My iPhone 5 is running the latest version of iOS 7 and recently it hasn't been charging with 3rd party chargers. I charged it on Saturday with a legit apple charger, but I don't have one at home so it died. It's been dead since then so today I went out and bought a real apple charger, but it won't turn on. I've tried pressing the home and power button at the same time and nothing happens. I have had it on the charger for about 5 hours and it still shows no signs of life. Should I just take it to the sprint store and have it replaced? Is there anything else I can try?

You can try recovery mode: support.apple.com/kb/ht1808.