I was having near exact same problem as you. I put my iPhone 5 into my pocket and then when I pulled it out to check the home screen it wouldn't turn on. I looked up forums on how to help fix the problem and all of them said to try the "hard reset." I couldn't perform the hard reset because my lock button does not work. I scoured the internet and eventually chatted with apple support but to no avail. I tried plugging in the phone for over 2 hours and tried every method. BUT I left my phone alone overnight and I tried to turn it on the next morning but nothing happened. So I plugged in my phone to my charger whilst holding the home button (not sure if that matters) and voila it showed the low battery screen.