Hi! Thanks for your reply.
Actually, I have replaced the thermal paste last night. The cooler yes, I did clean it and test it the very first day.
I spent the rest of the night doing back up of everything so I can try messing with the drivers, and eventually do a complete clean install as you suggested.
If eventually that doesn't help, I guess I can say goodbye to this notebook. But I still have hope. Somehow in the last few days, with all the things I've been trying, it works better. It doesn't turn off immediately (I've been doing back up for hours).