I replaced Logic Board and Comm Board Combination with known working replacement. When installed tried to power on, and screen would not turn on. Removed Comm Board and connected phone to USB port on computer, screen would turn on with Apple Logo for 5-10 seconds and turn off. Appears to be a hardware issue related to the Comm Board.

Tried different combination of Logic Boards, Comm Boards, and Mid Boards with same results. I thought that possibly the Comm Board was not being seated in the Logic Board correctly, or the ribbon connectors on the logic board were not seated. The only component that was not swapped out was the Touch Screen / LCD Assembly.

Can the Touch Screen / LCD Assembly short out the Comm Board, or cause an intermittent short that would prevent the phone from booting / turning on with the Comm Board Connected?

I just replaced the lcd screen on my phone and I nipped the flex cable that runs behind the lcd so i had to replace it too. Now my phone is doing exactally what yours is doing. It will only power up for a few seconds when it is plugged into the wall or computer. After a few tries it shows the charging screen with the lightning bolt under (The screen you get when your battery is completely dead). Have you tested to see what the voltage on the wires is with a multi meter? I am just in the midst of rigging up a samsung 3.7v battery to see if the battery has anything to do with it.