1. Are you currently using any sort of thermal conductive compound?
If not, get some, any kind will do. I recommend a pad of some sort as they are harder to **** up. This is based on your assumption that the computer won't start because of thermal issues. Before you apply it, get the purest rubbing alchohol you can find and use a lintless applicator like a cotton swab to gently clean the surface of the chip and the heat sink. Thermal conductive compounds, whether grease or pad, get down into the microscopic fissures in the surface of the chip and the heat sink, especially when heated. This chases stagnant air, which is a good insulator, out and replaces it with something with a much higher thermal conductivity, which in turn transfers heat from the chip to the HS and then to the air the fan pushes through the HS.
There is no reason not to use a thermal interface of somekind.
