After pressing the power button, when does the CPU, exactly, start working?

[wajed]

and which part of it exactly receives the foremost electron?

 

[MATLABdude]

Probably the part that makes sure that voltage and power levels are stable before enabling the rest of the CPU. That might sound somewhat cheeky, but it's true! (It's called a power supervisor circuit)

EDIT: The part about receiving the foremost electron is somewhat nonsensical since it's not like in a water pipe where one molecule of water makes its way through the pipe. You establish the electric field first (propagates outwards first) and then electrons jostle themselves around in a fashion not unlike a Newton's cradle:
http://en.wikipedia.org/wiki/Newton's_cradle

So the current starts up everywhere once the field is established. As for how the field propagates, well that goes along the length of the wire at some velocity a little less than the speed of light.

 

[harborsparrow]

you might want to read an electrical engineering book on sequential circuits vs. combinatorial circuits (i.e., the concept of clocking)