Not tested, but should work, and has the benifit of being simple. Use a relay with a two way switch (SPDT for the elecy people), connect the power good wire from the ATX to the relay coil along and the other end to ground. The connect the relay switch across the reset button so that, when the power is on the switch is open, and when it's off the switch is closed.
This should automatically restart the computer if the power dies.
As I said not tested and off the top of my head.