iPhone 4 won't boot with power cable connected?

Hello,

I have an iPhone 4 that would not turn on or be recognized in iTunes. I started the trouble shooting process. I disconnected everything plugged in a new dock connector and lcd screen. The phone booted fine. Tried the old dock connector and old screen...but nothing else hook up and the phone booted fine. To make a long story short I have tried new parts for everything one at a time. If the power ribbon cable is plugged in the phone is unresponsive (even to plugging in to turn on). If the power cable ribbon is out the phone work fine, with the exception of the power button :(...

I have tried a new power button too with no avail