My iphone 4 (3g, 3gs, 4s, 5, 5c and 5s) suddenly died. There was at least 50% battery left. I tried resetting it with the home button the lock / wake button and it didn't work, i tried charging it and it didn't help, until i read online that you can "Power Reset" your phone by holding the hold/wake + home buttons simultaneously for 30 seconds (until the apple logo appears)
Hope this video helps :)
NOTE: this technique won't work if your sleep/home button is broken. Try getting the button/s fixed first.
PS: don't mind the horizontal flip , I used my laptop to record this clip :)