|Also if the CPU fan stops running before the machine shuts down, suspect the fan's bearings are dirty or bad.|
If the CPU heat sink is loose, follow instructions for cleaning off old thermal compound and properly reapplying new compound.
If the heat sink is secure but the fan stops or is noisy, or is running slowly, it really needs replacing but some have reported success in removing or puncturing the paper label on the fan center and adding a tiny bit of very light oil to the fan's bearings. In these cases though, replacing the heat sink is the best answer though.
If none of these are the case, using a strong flash light, carefully examine the inside of the computer (unplugged) case to look for a loose screw floating around, missing hold down screw(s), partially unseated cards and connectors, wires that have been pinched or cut on the metal of the case or caught under screws or components, and fix accordingly.
You have to be a little bit crazy to keep you from going insane.