Place a multimeter across two of the four leads coming to the power switch. Press the switch and note which two leads are registered by the multimeter. Those are the two you need to solder leads to to turn on the lappie.
I used a docking station for an IBM R51 laptop with a power switch, so I didn't have to drill into my laptop. I drilled a hole in the docking station and put a female plug into the hole after soldering the leads. A male plug on the outside completes the circuit and allows you to easily remove the laptop if you need to. I also placed a momentary switch in parallel with the power switch and mounted in the dash so I can have control and also so I can hold it in for 5 seconds and force power of (windows you know ).
Use a small soldering iron on the switch if it is surface mounted. Tin your wires and touch only briefly to avoid frying your system...