Depending on the age of your computer it sounds like a capcitor issue, there was at least one batch of motherboards that failed early because of blown capacitors. The little "cans" particularly the green ones, look for these with bulging ends (the normally have a bare metal top with an "X" scribed on them, this X is a safety release I think.
Just as an aside blowing the dust out with an air compressor is a risky business, compressed air can cause significant amounts of static, you need to ensure everything is well grounded to prevent damage to the ram modules or the various processors.
(I work for a company that sells and services electronic standby power supplies)