A monitor has its own power supply and does not draw anything from the computer power supply. A typical 15" monitor draws roughly 100 watts, which is more than most computers take.
P (power) = I (current) * E (voltage) for DC circuits, but there's a fun thing called Power Factor for AC circuits that screws up the equation a little

For all practical purposes though you could figure out the power by measuring the input current and multiplying the input voltage. Of course, this is rather hard to do safely
A somewhat easier (though still time-consuming) approach would be to measure each of the DC currents
inside the case and convert them to power and add them all up. This will be close to the total power (the power supply is not 100% efficent though). It would at least be interesting to see how much power the motherboard uses versus the hard disk, floppy drive, and cd-rom. Has anyone actually done this before?
I'm looking at a hard disk right now that has a rated (max) current draw of 0.4 amps at 12v and 0.5 amps at 5v. This means that the max power for this drive is 0.4*12 + 0.5*5 =
7.3 watts! The most power is used when the drive is spinning up, not when it is moving along steadily.