PC start button effect from electrical point of view
In a PC with ATX power supply, a 5V rail (low current) is always on even if the PC is shut down. This is called 5V Standby rail.

The power button (on the front panel connector) is a logic input going to the front panel driver IC (ACPI). This front panel IC is on the 5V standby rail so it is always sensing the power button.

Once the proper logic level is detected on the power button, ACPI latches the ATX power supply pin "PWR ON" to ground and all other power rails on the power supply turn on. Once all the power rails are stable, "PWR GOOD" is asserted and motherboard starts using the power from the rails.


 

As it can be seen from the picture below, power button is a active low signal. When power button pin is brought to the ground potential, it is asserted.



Finally, you can connect your Raspberry Pi to the motherboard front panel connector like this:


Further Reading:
1. Power Management IC Simplifies ACPI Implementation
2. ACPI Spec