Oh yeah, that is the problem right there! Your cpu is overheating and tripping its thermal protection, causing the shut down after 5 seconds. You need thermal paste (or a thermal pad) to make good, non-conductive contact between the HSF and CPU. You can see what is happening without. You can get some at any local computer store or places like Best Buy or CompUSA.
You don't say if you have an AMD or Intel, but applying thermal paste is fairly simple. First make sure that both surfaces are clean. You can use 99% Isopropyl Alcohol to clean both. Then apply a small amount of thermal past on the center of the processor (about a grain of rice size drop) and no, more is not better. Place the HSF on the cpu in its correct orientation and fasten down.
Above all, make sure you are grounded when working with computer components!
If you have any question let us know.