Why wont my phone turn off or go to sleep mode?

Maybe the power button is not working the way it is supposed to work. Check if there are some piece of dust because after reading your question, I felt that power button is not functioning. Or there may be some software or hardware related issues. If your phone isn't more than 3 month old, instead of trying at home, you better take it to the service center.

There may be a piece in the power button that has fallen out. With my current phone (fake iphone 4) I wasn't able to turn on the phone and I thought it was a problem with my battery but it was actually just the spring that feel out under the power button. Once I put it back in place it worked normally. So if you've dropped it or had any major movement with the phone that could cause a piece to shuffle around. Or just a manufacturing problem that allowed a piece to fall out easily.