That can be it, I've had some of my computer's run into this problem which ended up being the power supply. It could also be your CPU you did say your heat sink get's hot/warm maybe it's thermal paste is a goner, which is causing it to overheat. Once a CPU start over heating your computer will shut down so it will not fry the system down. When it was on, an they used it did it shut down when they used something that loaded the process? Such as streaming video's? Running certain programs?