Oh Dear. There is a problem with a lot of the DV6000/ 9000 series of HP laptops, in that they screwed up the design and used nvidia chips, designed for a desktop in a laptop. Trouble is in a desktop, the chip gets up to working temp and stays there, cause it is continually cooled, however in a laptop they only cool when the processor needs it, as its quieter and saves power. So the Nvidia chip get hot then cold then hot then .... which wears it out, so it dies a lot faster. The way to prolong its life was an "upgrade" from hp that basically kept the fans on all the time. If your fan is running all the time, it sounds like it has the upgrade, although it shouldn't run when shut down. If its doing that, the fan supply is somehow bypassing the shutdown voltage control which it shouldn't cause most of the voltage regulators are shut down. I wonder if some clever sod hasn't wired the fan onto the battery supply ?.
Once shut down, to stop the fan, just remove the battery. To prolong its life, avoid switching it off and on, eg if you are going to use it on one day, leave it switched and avoid thermal cycles, eg heat up, cool down etc.
If you get bored, Google for Nvidia GPU problem.
Ken