Hi @ilayschipz
With the laptop assembled so that it can start, try connecting a ''momentary¹ earth'' to pin 5 of the keyboard cable connector socket on the motherboard to simulate pressing the power button and check if the laptop starts.
Unfortunately looking at images of the board that you posted I'm not 100% sure which end you need to count the pins from.
The 15 pin socket to the right of the 36 pin keyboard socket is marked i.e. a dot shown at pin 1 (left side in image) and the #15 shown at the other end but the keyboard socket only shows a dot next to the "KB" board designation and nothing at the other end, so hopefully it counts in the same direction.
''Be aware'' that there is +5V DC on pin 1 so be careful that you don't apply a direct earth to it as you may either blow a fuse on the board or damage some other component.
¹ momentary = length of time to simulate pressing the Power button to turn on the laptop but not long enough to simulate a force shutdown i.e. < 4 seconds