IPhone wont turn on?

i had this problem as well ! this is how i fixed mine : hold in the power button and the home button at the same time until the little apple icon shows up on the scree (MORE)
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Why wont your iPhone turn off?

Because you aren't holding down the power on/off button... On most it is the top and you just hold it down until your iPhone/iPod says, slide to power off. And then you slide, (MORE)

What can you do if the home button is broken on your iPhone?

To navigate without the home button, you will want to enableAssistiveTouch. This can be done by going to Settings > General> Accessibility, and scroll until you see AssistiveT (MORE)