Reset the motherboard (take it completely out of the case and reinstall it) and make sure there are no standoffs under the board (all of them should come up through the screw holes in the board).
The motherboard generally will not turn its green LED on if its faulty, and a faulty PSU generally will not provide any power whatsoever. So I am not sure on your diagnosis. I had that very motherboard give on to me, but it would not boot AT ALL and no power light was on.
Asus provides 3 year warranties on all motherboards, so you are still under warranty. Might want to try and RMA it just to eliminate that as an issue.