Ok, I'm confused suddenly as well and maybe the other folks were with you if you are indeed talking about AC. But I get a feeling that you are using some words here that don't really reflect the situation you are asking about.
If you have an ATX power supply, you shouldn't have any view of the AC power, unless you have taken the cover off. If you are talking about a similar power supply for arcade cabinets, these may have wire terminals for the AC in and the other voltages going out, but this would not be an "ATX" supply.
Without being able to accurately convey your situation, you need to take some pictures and post them if you want good advice.
The thing that causes the confusion is your reference to green and black wires, which on an actual ATX supply, will turn power on and off. But a 3 prong "mains" socket sounds like AC (and that you have the cover off of the supply).
If you are only powering a PCB and some lights, you should find out why the ATX PSU is coming on immediately (probably green and black jumpered as described above) and that is where you would put your switch. Then you could run any type of indicator LED ligthing from the +5 or +12 output of the supply.
Please take a picture so we know what you are asking.
RandyT