One of the rare times your CPU may fail is when your heatsink is full of dust and is not able to cool your CPU. Sometimes, if you CPU / heatsink heats up too much, the plastic that holds them together may fail. You can check that by cleaning the heatsink and then applying gentle pressure on it to make sure that there is proper contact with the CPU. SO if during that time your computer is stable, you know where the problem comes from!