Here's a link to the schematics for the motherboard.
On p.25 you'll find the pinout for the power button connector.
Pin 6 is the lead that connects to the motherboard's I/O chip to begin the startup process. Not sure if it will be an earth that is applied when the button is operated or the +3VPCU voltage, so first check what you test on pin 6 when the button is pressed i.e. either 3V battery or an earth.
Use a voltmeter and check for the battery voltage first when the button is operate and if there's nothing there, disconnect the battery from the motherboard i.e. no power connected and then use an Ohmmeter to check for an earth on pin 6 when the button is operated.
If no battery check if there is battery on pin 1. If no battery on pin 1 then you'll have to find out why there's no +3VCPU voltage.
If there is battery on pin 1 check if there is an earth on pins 4 & 5.
If neither battery or earth on pin 6 when the power button is operated, then the button may be faulty.
Time consuming but this is what you need to do when you're trying to find out what's happening. Hopefully you know how to read schematics and to use a DMM (digital multimeter)