Funny thing is, there are 2 signals to the CC analog board. the ADB power supply, which is nothing more than standy voltage to the ADB IC. then there is the power-on signal that brings up the main supply.

My guess, when you press power button the ADB controller responds and sends the PS-ON signal to the analog board, which brings up the entire machine. When you shut down, the ADB releases the PS-ON line and the machine shuts off.

Now, when pressing the power, and system NOT responding, either the IC is bad (which you replaced). or one of the traces to the ADB IC is open. I "think" Q1 behind the ADB port is responsible for pulling the PS-ON state.