It can also be the motherboard. CPUs rarely go out. Take a can of air duster, hold it upside down and blow it on the CPU heatsink. If it comes up then, it probably does need more thermal paste. If that doesn't work, trade out the RAM. If that doesn't work, its probably the motherboard. On some motherboards, when they go out you will see a kind of pink goo coming out of the top of some of the capacitors, or the tops of the caps will be starting to bulge up. They don't always do it, but its a quick easy check and if it is happening, you'll know immediately what the problem is.