First you must stop connecting power to your laptop. Disconnect the battery and the charger.
Second, you should remove the logic board entirely from the laptop. You have 2 parts: the main big board, and the smaller I/O board. The below applies to both parts. Don't forget to remove the heat sink and wipe away the thermal paste with IPA.
Now use good magnification to examine all the board. Minimum 10x. Better 20x or more. Take note of all corrosion spots and dirty spots.
Then soak the board entirely in isopropyl alcohol at 99% (at least 90%).
Scrub with a soft toothbrush all the apparent damage that you had noted before. And all the board if you want.
Dry over an air filter or in a toasting oven at say 50 degrees C for 1-2 hours.
Examine again using magnification. If you don't see anymore apparent damage, test the board again by connecting together the 2 boards, the fan and finally the power cable to the board (should light green). If charger turns green and fan spins, disconnect the power, connect the battery and try again to see if charger led will turn to amber.
Always test briefly, and disconnect the power ASAP.
If the above is successful, you can apply thermal paste to re-install the heat sink, and mount the boards back in the laptop to see if the keyboard or screen are affected and preventing the laptop from starting properly.
If the above is not successful, let us know here to, so we take it from there to try chip and board level troubleshooting.
Note that cleaning with IPA and drying is a minimum. It is usually better to clean using a pro ultrasonic to avoid failures in the near future.