Sorry to hear you are having such bother
There is a nice lil trick we call the paperclip test. If you use.....you guessed it a paper clip, to bridge the green and black wires in the 24 pin PSU block it will fool the PSU into thinking the mobo has told it to power on.
So you can now power it on and off from the wall socket. If your new PSU won't power on with this test then it definately needs RMA'ing. Obviously google the paperclip test before you try it just incase i got the wires confused at this early hour