Refer to the solution below to determine its connection line paths and connected components. In some cases like power switch terminal solder pads is lifted or the capacitor and resistor already been missing, you may need to use a microscope and sharp blade knife, then dig out the PCB layer where the capacitor or the resistor conductive connection and then manage to establish a solder connection on that spots.
Nokia E51 Power ON and OFF Switch Jumper Ways - Connection Tracks
If the above procedure failed you can directly apply a tiny magnetic jumper wire through to the power IC (AVILMA). However, this troubleshooting needs a good soldering skills because the power ON/OFF switch connection is connected directly to the power IC's solder ball bump number D9. Do not attempt to do it if your not good enough into soldering techniques. So Good Luck..
