It's stuck in blue screen because it's dying loading GPU driver. You have an X1600, they are all dead by now. They are far beyond their life expectancy. :) These were terrible chipsets when they were new even the ones intended for desktops - the ones for laptops are just frightening. Particularly ones with poor cooling design.
Usually the repair is replacing the dead GPU with a new one. None of that reflow/reball BS you read about online, the problem is not in the balls, it is in the GPU! With A1226/A1260, you can replace the G84-603-A2 and have a reasonable fighting chance it will work. With A1150, A1151, A1211, A1212, A1229, it is X1600. X1600 it is just dead and you will NEVER find a new GPU. Just reballed, remarked junk from Chinese sellers who claim it is new, when it is not.
If you do manage to find the one last X1600 remaining in the world that is new and try to solder it on - the Samsung VRAM on the board will die while replacing the GPU.
So for X1600 based anything, the only logical answer is to toss it in the bin. :(