IPhone shut off and won't turn back on?

I had my iPhone in my hand… And it had about 75% left. I put it down, and went to get something. I came back just two minutes later and it is off! I pressed the home button but nothing happened. I plugged it into the charger, as well as iTunes. Nothing happened! The phone also feels a little warm. I unplugged it but it still won't turn on.

On top of all this. My lock button does not work. It broke about 6 months ago. I need a way to fix this without that button.

If I was you I would either go on google or go to the shop where you brought your phone etc: o2, orange, vodaphone.
Hope that helps good luck xxxxx