can the arduino mega do this?

Too much info missing

I have a custom switch on my laptop

which laptop? what is a custom switch?

the input of the cable is 3.3 v

which cable? is that to power the Arduino? how many amps available? where does this come from?

turn my laptop on when ever it gets power

I don't get it. if the PC is off, does the 'custom switch' work? how do you plan to turn on the PC - is there a physical switch to flip?