If we assume that you have the pins on the FET connected properly (they are not identified in your circuit diagram), then the most glaring problem is that there is no connection between the Arduino GND and the GND on the ATX power supply.
Assuming, also, that when you connect the ATX power supply directly to the LED strip, it lights as expected.
The first pin on the FET is gate, the middel is drain, and the last is source. That´s what my datasheet says.
The strip works if I connect it directly to the ATX powersupply.
So I just have to connect the GND from the Uno to the ATX?