iphone 5 wont turn on or charge

Iphone 5 wont turn on or charge?

ok so my iphone 5 ran out of battery today and when i got home i put it on the charger and i waited for around 20 minutes and it still didnt turn on. i clicked on the home button and it showed it was charging so i let it sit for another 10 minutes. when i tried clicking the power button or the home button it was no longer responsive. i also tried plugging it into my computer but that didnt work. also i tried DFU mode and holding down the home and power simultaneously and still nothing, i can not reboot the phone and i have only had it for about 5 months. only problem i have ever had. Please help!!!

now all of a sudden it says on my computer that the usb device is not recognized and that it malfunnctioned