well it could be the logic board or something else really simple. Providing a macbook is a lot like a PC desktop in the terms of hardware then it could just be something is wrong with the case.
On a MOBO there are 2 pins that just need to be conected for computer to turn on and off. Normally this is done by the case completing everything. I have had cases go bad before and it was a pretty simple fix in a desktop. As for a laptop I do not have much experince playing with thoses on the inside but I know for the PC it is the same way. I have yet to really mess around on the inside of a mac but I am going to assume it is the same.
To test it you just have to find those 2 pins and conect them together by something like a screw driver. A quick tap is all it should take.