ATTiny85_ChangeToPulse.c

#include <avr/sleep.h>
#include <avr/interrupt.h>

void setup() {
  //intialize the input (the power switch)
  pinMode(4, INPUT);
  //intialize the output (motherboard power switch)
  pinMode(3, OUTPUT);
}

void loop() {
  sleep();
  //Pretend to press the power button
  digitalWrite(3, HIGH);
  delay(500);
  digitalWrite(3, LOW);
}

//Sleep code taken from https://bigdanzblog.wordpress.com/2014/08/10/attiny85-wake-from-sleep-on-pin-state-change-code-example/
void sleep() {

  GIMSK |= _BV(PCIE);                     // Enable Pin Change Interrupts
  PCMSK |= _BV(PCINT4);                   // Use PB3 as interrupt pin
  ADCSRA &= ~_BV(ADEN);                   // ADC off
  set_sleep_mode(SLEEP_MODE_PWR_DOWN);    // replaces above statement

  sleep_enable();                         // Sets the Sleep Enable bit in the MCUCR Register (SE BIT)
  sei();                                  // Enable interrupts
  sleep_cpu();                            // sleep

  cli();                                  // Disable interrupts
  PCMSK &= ~_BV(PCINT4);                  // Turn off PB3 as interrupt pin
  sleep_disable();                        // Clear SE bit
  ADCSRA |= _BV(ADEN);                    // ADC on

  sei();                                  // Enable interrupts
} // sleep

ISR(PCINT0_vect) {
  // This is called when the interrupt occurs, but I don't need to do anything in it
}