Immediate power-down after power-up is a symptom of the CPU Fan Off Protect, which is enabled by default if I recall.
Is the fan that you have on the CPU powered by a 4-pin PSU connector or does it go through the 3-pin header on the motherboard? If that's the case, make sure it is on the header on the top that is closest to the CPU socket. That's the one the board will shut down for if it is not receiving any RPM signal.
If it's on a 4-pin PSU connector, plug a fan in that header that uses the 3-pin connector and go into the BIOS and into the temperature/fan control section, and disable CPU Fan Off Protect, then save and exit, then unplug it. Of course, you will be shit out of luck if the fan on your CPU fails, but that doesn't happen often.
If neither of those work, it could very well be a flawed PSU. But before you make that conclusion, be sure that everything is seated correctly. All your RAM is tight and the latches are firmly in place, all your expansion cards are inserted properly and tightly screwed in, your PSU connector is on all the way, and you don't have anything obstructing the airflow to the PSU
