Auto Power on circuit when Electricity returns
Just as @AJN has correctly opined, take a closer look at the BIOS setup. The setting can be hiding in power management setup, chipset setup, SuperIO setup, or other places.
I've also seen machines where the setting was not available in the SETUP, or was available, but wasn't reliable (sometimes the machine wouldn't start). In such cases, it is possible to come up with auto-power-up circuitry. In the past, I have tested a trivial trick with a signal schottky diode - such as the BAT42/BAT43. It must be a Schottky, as you need its low forward voltage drop (as compared to plain silicon signal diodes). And it better be a &quot;signal&quot; diode = specced for low forward current, rather than some beefy rectifier (because schottkies generally have an ugly = non-zero reverse current). You need to connect the diode such that the power button live pin (having a pull-up to +3.3V StandBy) gets pulled down by some stronger power rail, while the PSU is off. The trick hinges on the fact that the power button input signal is active low - and as soon as the strong/actuated PSU rails start up, the &quot;button gets released&quot;. I.e. you don't even need to try timing the pulse or some such.
Let me hint at the connection in ASCII art:
PWRBTN -----|&gt;|------ +5V
I.e., the thin &quot;cathode identification stripe&quot; on the diode body goes to +5V.
You can probably use +12V or +3.3V for that same purpose. Obviously it wouldn't work with +5VSB :-) Speaking of an ATX PSU output braid, the Schottky cathode can go to a red, yellow or orange wire, but not to the purple wire. The power button signal is NOT present in the ATX PSU braid, it's a dedicated input on the motherboard, in the &quot;front panel header&quot;.
---- EDIT ----
So if this is a laptop, you will need to inspect the wiring of the power button, and if it principally matches the standard &quot;ATX power button&quot; function, you need to find some suitable power rail on the motherboard and connect the Schottky accordingly. You'll probably be messing among SMD devices anyway, so you may as well be interested to use a Schottky in SMD package, such as the BAR42. If the power button input follows some non-standard logic polarity or voltage level, you may need to modify the trick accordingly (such as, invert the signal somehow - with a FET, or a 74HC1G14 or some such).