Now IDK how these really work, or are laid out inside, but if they are anything like a motherboard, or GPU, or other common electronics with lots of voltage rails and a startup sequence....1st I would try and watch all the voltage rails come up in a logical order. Now if you know the IC's involved, and had a schematic (probably not) or map out some yourself, you might know the correct order for all the chips to power up.
Maybe it gets so far, some chip is unhappy, and doesn't allow the next parts to power up ? If all the voltage rails are good, and all the main chips have power, then the game can continue, and maybe some little external circuit is acting up.
Probably the worst thing will be if some big custom chip has a problem. Probably the only option for a hobbists, would be to try reflowing bad BGA joints.
As for all the software problems, yeah IDK how hard it is to get inside there and actually do anything. If you were lucky, maybe some little common MCU or EEPROM has a problem, and you could get a copy somewhere.