You are looking for a separate black cable coming from the PSU, either with or without a switch attached. It should contain 4 or 5 wires; brown, blue, white, black, and possibly green. This normally attaches to an on/off switch that goes to the front of AT cases. It looks like this;
If you find that cable you'll have to attach an AT switch to it. The PSU will fire right up. ATs don't normally need a power good signal from the motherboard.
Warning: The brown and blue leads to the remote power switch on an AT-style system carry live 110V (or 220V) AC power whenever the power supply is plugged in, even when the power is off! You should not work inside the computer with the power plugged in.
Warning: Switching the pairs of wires from one set of spade connectors to another will cause no problems as long as you exchange black with brown, and white with blue. However, if you accidentally make any other type of change, say, swapping black with blue and white with brown, the results will range from a blown fuse or circuit breaker, to smoke!