Re: Computer wont start up!!!
PSU = Power Supply Unit
Try a different power supply. If you have one laying around, just plug the main connector into your motherboard, 12v CPU power connector if your motherboard needs it, hard drive power connector, and others. You don't have to take the old one out of the case, just test it open. Plug in the new PSU and try to run the computer. If it works, take the old PSU out of the case and screw in the new one.
If you have a different stick of RAM, try that, also try reseating the RAM that you have and/or trying a different slot.
If the fans spin up and then the whole computer stops after a second or so, I'm thinking you have a motherboard short. Mine did the same thing when some pins on the case shorted it out (thought my new motherboard was DOA, but when I took the board out of the case, it ran fine). Try removing the screws holding the motherboard in place, lifting the board off the case, and try booting the PC while holding the board up. If it works, use plastic washers or another insulator around the screws and remove any posts that aren't used to hold it in.
Also try reinserting the CPU and heatsink, probably not the issue, but it's worth a try if none of the above work.
If you use an external (as in, not integrated) graphics card, take it out and reinsert it.
Check the motherboard for debris (like dust, as you originally said) that could be shorting terminals as well, if there's anything metallic in the debris, it could short the board. Many motherboards can and will detect shorts before they try and run the post test, and if they detect a short circuit the computer goes into a power-down state to prevent damage.