I have exactly same problem on my yoga 3 pro after getting it back from service for a faulty sdd. The power button does nothing, but has the white led light.
As you I go on using it by pressing the recover/boot options button. I do not think this harms the computer in any way, so I just go on living with this problem.
I dissasembled the PC to have a look at the connection of the button to the motherboard, but that dit not solve it.
(As a curiosity; the Type and Serial number from BIOS also disappeared after service.)