Get your multimeter and start testing diodes around the power jack and power circuits area.
Any diode that reads close to 0 in both directions is what you're looking for. If you find one, de-solder it, test it out of circuit to confirm. Once diode removed, laptop should power up (with proper polarity of course!!!). If you want to retain reverse polarity protection in the future, replace new diode. Rating of diode isn't super critical. It's actually considered sacrificial.