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You removed the power supply and plugged it into the outlet on its own. If the green light comes on, the supply is good (as you said below).
Sometimes, if the power cord is pulled out of the system quickly (or swtiched off from a opwer strip) after the system is shut down, the power supply can beep and the power LED can flash for a very short time afterwards. This happens because there was not enough time for the main voltages to decay before the power cord is pulled. It is not a failure, just an annoyance, and not the cause of your power up problem.