Why my iPhone does not turn on

My iphone started the last week to turn off and then back on on its own. Sometimes due to battery but some others I had it plugged in. Two days ago it turned off and I cannot turn it on since. I thought it was the battery so I plugged it in and it was just showing the apple logo, then black and the same thing over and over again. I tried to hard reset it with itunes and while itunes recognize the phone and it started restoring it says “Waiting for iphone” and after a while it gives me error 4005. I don’t know what else to do. Any ideas?