Also had this problem/symptoms, came here and decided to break down the phone checking every step the connectors were well connected. When the four screw metal cover came out I discovered the right side LCD display connector was loose, it had popped out when my daughter dropped her 4S, connected it back, reassembled immediately and the phone was back working.
I was lucky that was it, i've changed 4S screens several times in the last years (we now just have this one the rest are iphone 6) and that's a pain specially the corner screws! Didn't have to suffer that pain :)