Electric water pump or vacuum pump? OK maybe I'm out of the loop, but those are two things I've never heard of. Water pump is always run off the crank, and the vacuum is always created from the suction of the engine's intake.
DirtyBird has already said that he checked the fan, so that rules it out. That is freaking loud for a fuel pump, although if it is almost shot, it could be making a ton of noise; however, it would most likely be coming from the fuel tank at the rear.
The engine is not running, ruling out the alternator.
So, to sum up, in the average car, there are four electric motors which could make such a noise. They are the rad fan, the starter, the heater fan, and the fuel pump.
The rad fan (as I just said) was checked, and wasn't running. The fuel pump is most likely at the rear of the car, isolating it from the rest of the motors, making it fairly simple to figure out. That leaves the heater fan and the starter. Now don't quote me on this, but I think the heater fan is inside the passenger compartment, under the dash. This leaves the starter as the last electric motor which could be quite loud outside of the car. The starter, when running at full speed (which is normally never heard), does sound quite similar to that. The burning smell that accompanied the noise also makes sense, as the starter would be starting to "burn up" from spinning that fast for more than a few seconds.
DirtyBird, see what you can do with this info. Don't make me have said all this for nothing.
