Surprisingly, I got two suggestions off the NZXT web that I sort of liked. First is to try resetting the CMOS, which never hurts. (Pull the battery out for 30 seconds.)

The second good one was this,

Jump-Start with a Screwdriver

Just to rule-out the possibility that the PWR_SW cable is damaged or defective, we can easily jump-start the system by bridging the PWR_SW contacts through a screwdriver. This is trivial and a useful skill to have.

Disconnect PWR_SW connector from the motherboard.
Using a screwdriver, bridge the PWR_SW pins on the motherboard. This is done by using a fat enough screwdriver that the metal tip forms a physical “bridge” between the pins, through which electricity will flow.
Remove the screwdriver immediately after start.
The system should power-on if all is well.

The main suggestion I was going to make was, once you rule out the more obvious causes, it's worth pulling all the parts out of the case, to see if they will boot up separately. It's not that uncommon for a motherboard, or, more often, something like a CPU heatsink support bracket, to short out against the case, which creates a lot of weird electrical problems on the motherboard.

And, even if the power supply is brand new, I would want to see if it boots up with some other compatible power supply. (It can be smaller, because you dont need to test it under load. You just want to see if it boots up and runs normally. Maybe you can borrow one out of another computer temporarily.)