My iPhone turns itself on after I turn it off

Did you already try to reset your device by holding the sleep and home button for about 10 sec, until the Apple logo comes back again? You will not lose data by resetting your phone.

If this does not work, try to set it up as new device, explained in this article:

How to back up your data and set up as a new device

All the research I have done points to the dock connector in the phone, read they were exchanging them at the apple stores