I'm not sure if this helps since I wasnt entirely sure what you went by bracket but i'm assuming the frame surrondung the glass/LCD assembly . I wouldnt really recommend do that as its much much better to just to return the damaged part. If this isnt ideal then yes you can replace that frame with heat and readhere it using my personal favorite. Serious Glue, as it works really really well on glass.
Im not sure if this helps, I know computers will shut off if overheated. If I were you I would open the laptop up using a guide. Check the condition of the thermal paste on the CPU and replace it. Also be sure to blow out some of that dust once you're in it. Hope it helps, Good luck!
I believe you would have to replace the LCD, I've had this issue in the past and I believe that's what I did. There should not be an "LCD Switch" and as for the stripped screw, I would try using a flat heat. I use two methods of removal of stripped screws. I either solder something into the screw and then remove it or I Dremel a pattern and unscrew it with a flat head. I'm not sure if this helps but good luck!
So, after tearing my hair out for 2 days. I finally found the issue. It was this battery sensor on the side, it was covered in corrosion. I unplugged it and replugged it after cleaning it with 91% alcohol.