The subject behavior is likely a computer BIOS problem.
Your BIOS may be set to Stay Off or Last State.
NOTE: The actual names in the BIOS will vary by manufacturer and language.
If the BIOS setting is Last State and the system is shutdown without pausing at the It is now safe to power off your computer message, the Last State defaults to Stay Off.
To workaround this behavior, configure the BIOS so the computer always starts when AC power is restored.