Hi. Don't mean to bump an old thread but I'm not sure if you ever found a solution and this is one of the first results on Google so I'm posting here to help you or anyone else that has this problem in the future. I recently had the same problem and fixed it for rather cheap. Mine's a N53SV and on that at least (should be the same for N53s, N53SN, and N53SM as well) there's no need for a costly replacement of the entire palmrest. The PCB that controls the power buttons comes off of that and a small cable detaches from the PCB. On mine it was a little white ribbon cable with a blue bit at one end. All of these are replaceable independently and are much cheaper than the whole assembly.
You can use the part finder at
http/www.asusparts.eu/en to locate specific parts for specific Asus laptops.
The part in question worked like a charm was this one:
http/www.asusparts.eu/en/Asus-14G124030186
on a side note there are little brown clamps that hold said ribbon cable both on the PCB and the motherboard itself. Whatever you do don't damage those as I've not been able to find them for sale independently anywhere and should one snap off (like the one on my motherboard side did) you'll have to jury rig something to hold the wire in place (i used some thin cardboard)