This probably doesn’t have anything to do with your screen. It’s your internal hardware. If it is still a fully original phone, you need to realize it’s +5 years old. Parts wear and can break down after a long while. Make sure your phone’s storage is not completely full, as this can slow down your phone. If this doesn’t work, try software-update (you actually need to do these always, anyways :D). If it still doesn’t work, make a back-up, reset the phone, and put the back-up back on there.
I think your antenna is damaged. Make sure you have no thick phone case around your phone. If it still does not work properly without those, you may need to consider getting a try on repairing the antenna. This because you mentioned that your friend with the same sim-card had a good stable connection. So it must be a hardware problem.
Maybe there is a problem with your internal power supply (battery & wiring). Check if your battery connector is still properly in place. If yes, you maybe have a damaged or old battery. It could be that your battery reached the end of it’s life, and it’s not able to deliver enough power to get the screen to work.
First of all, a cpu temperature above 100 degrees is not normal! I think a heat sensor is broken, because you mention that your cpu is fine when the fans go on max speed. The computer is supposed to run those fans at max speed automatically if the cpu get’s a high load (what increases the temperature). Another thing that could be a problem too is that your airflow isn’t that good anymore. It maybe doesn’t seem like it, but maybe one of your fans (or fan motor) is damaged?