Have you replaced the thermal paste?
Yes, as I have said above. I have tried everything that would make sense. I am suspicious about some other hardware damage, like CPU, GPU, maybe chipset. It used to overheat that much that the motherboard has literally turned brown, almost black on couple of places (around CPU for example). But again, I think that if something was really broken, it wouldn't work any way. Now I have a new issue. The screen goes black, but I can hear the fan and the power button led is on. Caps lock, charging and HDD leds don't work at all. Then after 30 seconds to 1 minute it comes back. Yesterday I have left it on the window, so that it cools even better (it was around zero degrees celsius outside), and I think that temperature sensor has gone to hell, because the Temp1 (don't know what that is) and GPU in SpeedFan go to 93 degrees celsius, and in the next moment, it's 81. I would understand if it was otherwise, but I don't get this at all. Again, it went completely off after some time, so I'm guessing it has nothing to do with temperature. I heard that some laptops automatically shut down when they reach some potentialy dangerous temps, so if the sensors are broken, it might be that.