If the cpu core area is clean, you only need one drop of thermal paste in the center. You can install the heatsink and let the pressure spread out the paste, or use a single edge razor blade or business card to spread it yourself. Too much paste is worse than not enough. A thin layer barely visible is ideal. If the laptop is together and posts for a few minutes, I would wait for your neighbor or someone else to fix it. I've got twenty years experience building computers, but I hesitate to take apart any laptop unless I have no choice. Too many fine wires and connectors.