Is it possible to repair power button?

Using a heat gun you can soften the glue that holds the button shell to remove it to gain access to the now broken wires so you can replace them. you will still need to splice the loose tail you have with the logic board connector to what you've attached to the button just make sure the wire routing is not haphazard as you can create a short or sever the wires again. Use the heat gun to heat up the glue to re-attach the button shell, if needed use some hot glue.