Hi, don't want to bring your hopes down, but the big graphics card chip (the green BGA pacakge soldered on the MB), its solder joints tend to fail because of thermal recycling of the component , i.e when it gets hot and cool down the solder joints under it are mechanically stressed and may fail, if you exhaust all your options in power supply troubleshooting, this could be the problem and it will need to be reworked using a BGA rework station.
Other thing to check is the LCD display inverter, not sure if you have checked that the laptop boots to an external monitor or not so give it a try and see how it goes.
Keep up the good work as its a good learning experience.
Best regards