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You will be using compressed air and a vacuum to remove the majority of the dust from the inside of your computer, so set up an area that you can blow dust out without worrying about getting other things dirty. A garage or workbench is a good choice, or you can go outside if it's a dry day. Try to set up a table so that you can easily access the computer without having to bend over or set it on the ground. You will need a Phillips screwdriver, compressed air (either in a can or via a compressor), a small vacuum that can fit in narrow crevices, a toothbrush, and 99% isopropyl alcohol.  Do not use an old vacuum with a metal tip, as these are usually poorly grounded and can damage your components. The best option is a newer handheld vacuum with an extendable plastic hose. The toothbrush should have soft bristles, and should be new. Shut down your computer and disconnect all of the cables on the back. Make sure that the monitor is unplugged, and that any USB cables, Ethernet cables, speaker cables, or anything else is unplugged as well. Flip the switch on the power supply and then remove the power cable. Place the computer on its side on your table or workbench. Make sure that the connectors on the back are laying closest to the surface. These connectors are attached to the motherboard, and can help you ensure that you remove the correct side panel. Remove the screws that hold the side panel in place. These screws can be found along the back of the computer. Most modern cases have thumbscrews that you can remove without tools, though you may need to use the screwdriver for older cases or thumbscrews that are too tight. Set the screws aside so that you don't lose them. Depending on how long it's been and your environment, you could be greeted by a pretty gruesome sight. Dust has a tendency to collect and cake on your components, and the entire inside may be covered in a fine layer of gray. Use your vacuum cleaner to do a pass over the interior, sucking up the large bits of dust from the components and crevices. Be careful not to strike any of the components with the vacuum tip as you move it across the interior. Many components inside are very fragile, and bent pins and connectors can render your hardware useless. Take your can of compressed air or air compressor and blow out the hard to reach crevices. Use the vacuum to help reduce the amount of dust that scatters in puffs.  Avoid long, sustained blasts, as this will make your can of compressed air too cold to hold. Don't blow compressed air on your fans. Blowing on the fans can make them spin faster than they are designed to, potentially damaging them. Use the vacuum to remove the large amounts of dust on the fan blades. Dip your toothbrush into the alcohol, and gently scrub the dust that remains off of the blades.  You may be able to access the fans easier if you remove them fist. You will need to remove the screws that secure the fan to the chassis, and then disconnect the cable that connects the fan to the motherboard. Make sure that you note where the fan was plugged in so that you can easily reconnect it when you're finished cleaning. Make sure to reattach the fan in the same direction that it was originally installed. Fans blow in one direction, and reversing the direction of air flow can significantly impact the cooling of your machine. Most fans have an arrow printed on the top of the housing that indicates which way it blows. While a general vacuum and dusting is usually sufficient for basic cleaning, you'll want to remove individual components to really get them sparkling again. Make sure that you are properly grounded before touching any of the internal components. When you remove the components, set them on an antistatic surface, such as wood or rubber.  You can remove the graphics card by removing the screws that secure it to the case, releasing the tab underneath, and then gently pulling it straight out. You may have to disconnect power cables in order to fully remove it. Set the graphics card on your cleaning surface and use the brush and alcohol to remove stubborn dust. Removing the hard drive and any optical drives can make it easier to clean them, since they are often tucked away in hard-to-reach bays. Removing these drives typically involves opening both sides of the case so that you can reach the screws securing each side of the drive. Most optical drives are pulled out of the front of the case after the screws have been removed. Removing the CPU cooler will allow you to clean out the cracks in the heat sink, as well as brush the dust out of the fans. Heat sinks attach in a variety of different ways, so make sure to consult your documentation before trying to remove it. Some require you to remove a bracket from the backside of the motherboard. If you remove the CPU cooler, you will need to apply a new layer of thermal paste to the CPU before reattaching it. Depending on your case, you may have some grates for fans and airflow. Use your compressed air to blow out from the inside of the case, and then run a feather duster over the grate from the outside.
Setup an area where you can blow dust. Gather your supplies. Power down the computer and unplug all of the peripherals. Set the computer on its side. Remove the side panel. Do an initial vacuum. Use the compressed air to blow dust out of crevices. Clean the fans with the vacuum and alcohol. Remove components for deep cleaning. Dust all of the grates.