Set the ATX option in your BIOS to boot up after power failure. Have the signal on the shutdown controller triggered by a source that's on when the car is on.
If you don't have that BIOS option, you can wire yourself another ATX power button, or you can fake it with the kill switch on the shutdown controller (requires another manual cutoff switch. car turns on, shutdown controller gives power to PS, flip switch to turn off signal source, shutdown controller thinks car is off, begins countdown, hit kill switch, it immediately sends ATX pulse, starting your computer, flip switch to on, shutdown controller goes back to the 'on' status).
(that last bit, in summary is:
1. turn on car.
2. flip (normally on) switch off.
3. press kill button.
4. flip switch on.
The BIOS setting is the best though.