You obviously do not get a charge light or any response when plugging in the machine? It will be the mainboard that needs to be replaced. Potentially the battery but I assume you have tried plugging in the Charger without the battery connected? Try minimum config, which means unplug all removable components from mainboard (remove LCD cables, KB cable, KB backlight, wifi card if removable, battery etc.) and leave only charging port and if separate the power button ( some laptops have separate Pwr button board) and see if you get a response from charger. If you do add each component one by one until symptom returns. If still no response it will likely be a motherboard that needs to be replaced.
Did the flap physically snap? If yes you only option is to buy a similar main board or laptop that is broken/liquid damaged cheap and move a flap across, it is possible to re attach them but quite difficult. If it has just come off, it is possible to get these to slide back on.
The iphone screen home button connects through the screen connectors. There is also a small connector on the screen near the home button. Check the small connector, can’t remember if it was to the left or right of home button (left I think) but it clicks onto a connector that is glued to the back of the screen. If this is OK, re- seat all your connections that go to the screen, be careful though, they should not be forced and should click in with a small amount of force when lined up correctly. Hope this helps.
Sounds like you may have cooked the display or somehow damaged the ribbon cable, maybe with too much heat. Would suggest the only option is to replace the screen. I am sure you have tried re-seating the screen cables?