I would test the momentary switch to see if it interrupts a current, or switches a digital signal.
Then I would make it so that after the main power is turned on, there might be a small delay(1 second), and then the 2 momentary buttons would be held down using a relay, IC, or what have you.
To turn a monitor or computer on, you simply need to press the button. To turn it off however, you need to press AND release the button.