The ATX power supply will not turn on until the motherboard pulls the PS_ON signal low.
Some motherboards allow you to set a automatic power on after power failure. By enabling this feature when you turn the cabinet on via via your main power switch (powerstrip) the PC will come on automatically.
If your BIOS doesn't have this feature you need to pull the PS_ON signal low yourself. The PS_ON signal is pin 14 (green wire) of the ATX power connector. The best way to do this would be to remove this pin from the connector (you can probably do this using a needle, paper clip, or other sharp pointed instrument) and connect it to one of the GND pins (black wires) on the ATX connector (pins 3, 5, 7, 13, 15, 16, or 17). This will tell the power supply to be on all the time so whenever AC power is applied it will turn on.
Hope this helps.