So, with nothing else connected except for the CPU, CPU cooler, memory and graphics card, the system will not power on? No drives connected to the power supply OR SATA headers. None of your NZXT hardware connected. No case fans. Only CPU, cooler, memory and grahics card, would leave the side panel off for now, still no power at all?
I would strip down to that setup, disconnect the power from the outlet, remove the CMOS battery for about two minutes and press the power button for about ten seconds. Then return the CMOS battery to it's position on the motherboard making sure the correct side is down, plug the power back in to the wall socket and try to boot with a minimal setup. If it turns on, then power off and connect the OS drive and try again. And so on.
Power supply is not a very good model, but it's not a horrible one either. Not a unit I would recommend for use with a system of this caliber in any case but unless it's just one of those things, and it's not working due to a defect, I'd suspect something else. Certainly it COULD be the power supply though, as I doubt that unit can actually sustain it's rated power, but you're not trying to do that anyhow, just trying to get signs of life.
If you have, or can get a multimeter, you can certainly test it for basic functions.
https://www.youtube.com/watch?v=ac7YMUcMjbw