Brush and gently vacuum
Before opening the system, I recommend vacuuming the dust and debris from the fan filters and other vents. Next, quickly wipe down the external surfaces with paper towels lightly dampened with spray cleaner. Don't spray the cleaner directly onto any surface! The liquid could pool somewhere and cause a short.
Now open your PC and inspect its guts. The dust filters on my dirt-encrusted case did a nice job of keeping large debris out, but plenty of dust had still slipped in and built up on the heatsinks and on all of the flat surfaces. To clean the inside of the system, I started by vacuuming up all of the loose debris and ridding the flat surfaces of as much dust as I could. You can do the same, but be careful: When vacuuming inside a system, don't use a big, high-powered vacuum and definitely don't drag the hose or nozzle along the surface of any circuit boards. The last thing you want to do is knock off a surface-mounted capacitor or resistor and suck it up into the vacuum. Use the vacuum sparingly, and focus on gobbling up the largest bits of debris inside the case and on fans, heatsinks, and the like.
When your intake vents get clogged up, negative air pressure generated by exhaust fans within the case will pull air through every hole in the case, eventually clogging them with dirt, too.
Remove and reseat cards and cables
Once you've vacuumed up most of the dust and dirt, remove the add-in cards from the system (on my test PC, only a sound card and a video card fell into this category), and reseat all of the power and data cables on the drives.
Removing the cards makes them easier to clean. It also gives you a chance to counteract a phenomenon known as "chip walk" (or "chip creep"), which causes cards and connectors to come loose over time. As the components in a system heat up, they expand slightly. And when they cool down, they contract. Over many cycles of expansion and contraction, add-in cards and socket-mounted chips can creep out of their slots or sockets; reseating the cards and connectors ensures that they remain properly connected.
While the cards are out your PC, I recommend giving everything a solid blast of canned air. If you're cleaning a particularly dirty system, you may want to do this part outside, because the dust will fly everywhere. Shoot the canned air at all surfaces and into all fans and heatsinks--in the direction opposite to the direction of the fan's airflow, if possible. If, after vacuuming and using the canned air, you still see dust on a surface (this is common inside thin heatsinks), use the brush to clean out and dislodge the dust, and then fire away at the surface with the canned air again.
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