Why does my iPhone 4s turn off randomly?

Even if its battery percentage is at like 60% or even full. And when I try to turn it back on, it doesn't. If I tried to charge it, nothing happens. I tried calling it with my other phone and it can still be contacted and that just confuses me even more. It still heats up like it's turned on too. I can only turn it back on many hours after but it has drained all its battery. The sign that says the battery is empty and that I need to charge it appears. The lesser battery percentage, the sooner it recovers (still drained) and the more battery percentage the longer it stays dead. Someone knows what I mean? Please help:)

A faulty switch? Advice the closest apple store or go on line and ask apple.