How to fix power button?

It is most probably this problem :

Устранение неисправности клавиатуры

See also :

Устранение неисправности клавиатуры Asus Zenbook UX31A

If you may have slipped any liquid on the keyboard, it may become not responsive. As the only option to power up the laptop is via pressing the 'power' button on the internal keyboard, you won't be able to turn on the laptop.

Removing and cleaning the keyboard may help but not necessarily -- this laptop's keyboard is a thin thing and you can't really clean 'in-between' its layers.

You may want to replace the keyboard as the first option.

Or if you reasonably suspect that the liquid could have gotten further down from the keyboard unit, you may want to 'ring-out' your motherboard first.

As to me, I've firstly checked that the motherboard was OK, then replaced the keyboard. Everything started to work as a chime.

If your keyboard works but the touchpad doesn't - check that the touchpad wire is firmly connected (from memory, to the back of the keyboard rather than to the motherboard -- but I can't remember for sure). Sometimes the connection gets lose (and may especially get lose while you are working on replacing the keyboard).