KyrioDynami :
The NZXT S340 doesnt have a reset switch so that is another problem.
You are right, there is no reset switch.
If the power led shines, without the power on, I suspect you have mixed up the leads for the combo power switch and the power led.
Double check which pins are connected. It can get very confusing orienting the pins on the motherboard header.
On the possibility that the leads are mislabeled, try connecting different pair combinations to the pwr sw.
The led is not a required function.
If you get a combo that works, connect the remaining two to the pwr led leads. If they do not light switch them.
The led leads do have polarity sensitivity.
Nothing permanently bad happens if the front panel leads are connected wrong.