Hook your charger to the PSU first, then turn the PSU on.

Many chargers have ripple suppression caps on the front end and, when discharged, represent a sufficiently high current sink to trip the overload circuitry of the PSU. However, the ATX Design Guidelines state that the PSU should be able to power up and stabilize with a 4700 uf capacitive load on the 12v rail -- this is due to the high capacitive load on the current motherboards. Once the PSU has stabilized, high current sinks are then identified as a possible short, the overload circuit captures and the PSU shuts down.

This solves the majority of Power_Off situations when the charger is attached, but if not, you may have to look to another power source.