Phone rebooting after shutdown

I have just changed the battery of an I phone 4S that my son had discarded with a dead battery. Everything works now fine, except one major problem (possibly older). The phone reboots after an attempt to shutdown, unless the operation is performed with the dock cable attached either to a live USB port or a live wall charger adapter. When plugged to a live power source such as the USB port of a computer, the shutdown is successful, but the phone reboots as soon as I shut the computer down or disconnect either the dock connector from the phone, or the usb port from the computer. I have tried software restauration, even just downgraded to IOS 6.1.3 from 9. something whatever the latest version for I phone 4S from Itunes, several hard resets, DFU mode, etc, no change. I have read here that changing the dock connector on the phone could be a fix, but before proceeding I would like to get some sound advice.