I ordered a doner laptop of a similar model with a damaged screen. unfortunately, deposited appearing cosmetically identical, the two screens were incompatible.
I then started testing various aspects of the new machine and found that it wouldn't power on without the presence of a smaller secondary board at the bottom, which connects to the main battery. This gave me an idea. I swapped just this smaller board into the old machine and it worked! So it wasn't the entire motherboard that blew, but rather this smaller board that contains some kind of additional power circuitry.
I inspected the old power board one under my microscope but couldn't find any visible faults or shorts with my multimeter. I also removed and tested the capacitors, which were fine. So it's probably one of the more complex power IC chips. Which one it is, I have no way to tell. It's otherwise I going cosmetic condition.
I also found the source of the high frequency noise. It's not the speakers but the LCD inverter. Confirmed this by unplugging the speakers and could still hear the noise. I kept searching for it with my ear until I found that it was the inverter. This vintage of laptop would mean that it's a CFL inverter. I'm not sure what to do about this noise.
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