Home and power button not responding on iPhone 6?

All of a sudden, the home button on my iPhone 6 stopped responding, so I figured turning it off would work. So I pressed the power button and turned the screen off. But when I went to turn the screen back on, pressing the home and power button didn't work. So I plugged it in and that still didn't light the screen up.
I've had this phone since September 2015. This is the first time this has happened.

Added (1). So now I can't turn my phone on at all. Anyone know what to do?

Press the home button and power button together at the same time and hold. May take about 2 mins

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