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cloud9ineteen 
If the other tips don't get it fixed, also check whether it persists if you don't have the Power button connected to the motherboard. Instead of using the Power button, try making a momentary electrical connection between the Power Button pins on the motherboard and see if it runs and doesn't do the Standby trick.
If that helps, then I'd suspect there's something fishy about the power button, mechanically/electrically.
Bigger picture: you might consider replacing the whole motherboard if it gets to be too much of a nuisance. Also, could the power supply be having a problem? How old is it, what brand/model/wattage, and what hardware is it supporting?