When a laptop gets real hot, it usually means its getting over heated. What I would do would to open the device up to where you can see the motherboard and see if there are any signs of burns or liquid damage. If it all looks clean then you might try redoing the thermal paste on the heat sink. If that fixed the overheating issue but the display still does not turn on, try connecting the laptop to an external monitor, if there is still no display then the video processor on the motherboard is probably faulty, if there is video on the external monitor then I would reseat the lcd cables on both ends, the motherboard connector and the lcd connector. If this does not fix it, try a replacement LCD or take it in to a repair shop.