Have you tried to connect it to the charger? That works for most phones to wake it up or, when the battery is empty, to start the phone when reaching a certain charge.
If that does not work you could short-circuit the power button: To do this you need to do some disassembling. I am assuming that the golden plate with the two contacts (just below the blue and red wires on the right side of [link|https://youtu.be/QOiBytB9po0?t=217|this video|new_window=true]) is the contact for the button to the motherboard. If you peel this off from the other side, re-insert the motherboard, battery, and temporarily connect the display you might be able to short-circuit that contact on the motherboard. But those are some "IFs" there.
Try the charger first ;)