Can I boot my mac without pressing the power key?
shutdown -u

I tried the 'Start up automatically after a power failure' but after a cold shutdown, a power cord disconnect/connect did not boot my computer.

The automatic power on only works if the power was cut. You can induce this behaviour using the command shutdown -u now. According to man shutdown the -u flag does the following:

-u: The system is halted up until the point of removing system power,
but waits before removing power for 5 minutes so that an external
UPS (uninterruptible power supply) can forcibly remove power.
This simulates a dirty shutdown to permit a later automatic power
on. OS X uses this mode automatically with supported UPSs in
emergency shutdowns.