Hmmm... I don't think it's the fuel pump... It is fairly loud and it seems to come from inside the dash and not from under the hood. I can't say for certain that PiinkSox has the same issue I have, but it does seem very similar.
I usually turn the key back when I hear it.. and it stops. When I turn the key forward again it's gone. Maybe I should try to see if I can keep the key forward when it buzzes and see what it does. If it's the fuel pump then it shouldn't last long and the car will start right? If it continues to buzz for a while then I assume it wouldn't be the fuel pump.
It's just really hard to remember to keep the key turned forward. When my car makes a sound like it's in pain, I try to take away the pain.