Just plug it in. If it doesn't detect a power button it will turn on automatically. However, if you turn it off you will not be able to turn it back on again until you unplug the battery and plug it back in. You will be able to restart it, but not shut it off. If it dies you will have to unplug the battery again to get it to turn on.
If you plug it in and it doesn't power on then you need to unplug the battery and plug it back in.
If it still doesn't work you need a new logic board.
If it does work you need a new palmrest/keyboard.