Sounds like the PSU is checking the relevant connections, finding that there is a problem and shutting itself down.
1) Check the 24 pin (the big power connector to the motherboard), is securely fitted to the motherboard.
2) Check the smaller CPU connector is correctly/securely connected to the motherboard.
3) The wires to the front of the case, e.g. power LED, HDD LED, double check vs the motherboard instructions. Why because as others have said it easy to get mixed up there.
4) This is the important bit, sometimes the wiring for the case has a reverse polarity issue, what you have to do is turn the power LED wire upside down etc.
5) Is the CPU fan connected to the CPU header on the motherboard?
6) Stupid question, I presume the memory is fitted securely and correctly to the board, if the board does a self test and find this missing it may shut down. TRY ONE STICK OF MEMORY AT A TIME.
Regards
Von