Chosen Solution

After getting error 4013 and try many times without success, I loose the phone to service, the board, after light clean with spirit, the phone does come up and shows itunes logo, but could not be detected at all, I still try another charging point, the story goes the same.

Was the board water damaged? Try a cleaning with isopropyl alcohol, if it shows up the iTunes screen then iTunes should detect it. Try DFU mode: http://www.iphonehacks.com/put-iphone-in