If you want to know if your A1342 top case (power button) is faulty you have to start up the machine without the top case connected. To do this:
1- remove the macbook bottom cover (8 philips screws)
2- disconnect the top case ribbon cable from the logic board (check the ifixit repair manual for the Macbook white uniboy A1342 to locate the connector but it's really easy to find)
3- locate the 2 power pads on the logic board, they are near over the top case connector: look at ABCellars pict to locate the power pads:
Minimum components needed to power on?
4- with the ac adapter connected to the machine trigger the 2 power pads with a small flat metallic screwdriver.
5- the macbook should start up and boot the system
6- (optional) if you have access to an external USB keyboard and a mouse connect them to the machine before starting the machine.
7- if the macbook works as it should then the top case is faulty.