Very interesting - would you be able to post more details?
It's highly platform-specific, but here is the general principle:
When power is available, there will be a standby voltage present
somewhere on the board at all times, to support Wake-on-LAN, wake-on-
Bluetooth, etc. On a desktop PC, there is an explicit +5Vsby output
from the PSU. On a laptop, you either get lucky with the silk-
screening or you probe around the board with the machine switched off.
Start with the Vcc pin of any small microcontroller you can observe.
The line should also be available at any internal PCI, PCIe slot, I
believe.
IIRC when I had an Eee 2G Surf, it provided USB bus power at all times
when AC was present (to hell with the spec, full speed ahead, right?).
So that might be a convenient takeoff point if you have no luck
elsewhere - it won't be available when the unit is running off
battery, though.
The power button on a laptop is typically an active low input to some
kind of power management microcontroller. Pull it low, the machine
starts up. Unfortunately in most cases it is not enough to simply tie
that line low because holding the button low typically invokes an
emergency hard shutdown in the case where the main CPU is irrevocably
crashed.
So get your 8-pin PIC, or your 555 rigged as a one-shot. Configure it
so that as soon as power is applied, it will wait (say) 1 sec for
everything to stabilize, then pull the power-on line low for 500ms,
then release that line and go to sleep forever. Power the micro/555
from the standby voltage and connect the output to the power control
pin.
An RC might sometimes do the trick too, but I haven't found this to be
very reliable in the past (too iffy, especially if there is a brownout
or power glitch that leaves the PSU in its switched-off state, but the
RC charged above the Vil voltage of that control line).