Power / Eject Button Circuit (Xbox Original)
The power and eject buttons are fairly simple. They are buttons on a front PCB that connect to the motherboard and go to the SMC PIC chip via a few resistors.
When the button is pressed the SMC sees the low pulse and powers on if all is well.
Thanks to the user Dave420Fun on Reddit for this schematic and explanation.
Check for continuity (or 10k resistance) from the header where the front power eject board connects on pins 2 and 4, to the SMC PIC chip (rear left) pins 5 and 18.
It is common for the traces which run along the perimeter of the board along the front and left sides to rot.
You can also test if shorting pin 18 (power) on the SMC to ground, to simulate the power button being pressed. If this works but the power button does not it is likely trace damage or resistors.