Hi, I use Isopropyl Alcohol for cleaning.
I would be suspicious that the the heat sink is not attached properly if One of the four pins does not go in as far as the others. In my Experience they always sit at the same point. Since You are going the Newegg route for the Arctic Silver, Why not order a new heatsink as well.
Notice that part of the heatsink at the bottom of the image with the arrow pointing to it. If one of those did not go through the hole in the motherboard the heatsink will not be seated properly. I have seen cases where one of the two halves went through the hole and the other one got bent over on top of the motherboard.
There is a possibilty that the CPU is running hot and has throttled back the speed to protect itself. I have seen Older Dells where the heatsink came loose, Dimension 2400 for example, and the computer would not even stay on long enough to finish the P.O.S.T. process.
The heat sink will not feel hot if it isn't attached properly.
I agree with Rotor123. Check that both sides of the pin clip (for lack of a better term) are through the hole. If the heat sink is cocked even slightly, it will overheat. Without the heat sink to cool it, it is possible to overheat in seconds, and melt down within a minute or two. I booted one without a heat sink once just to see. Put my finger on the CPU and booted, within seconds it was too hot to touch