Really Puzzled

I have a 1997 Chevy Lumnia with 63,000 miles on it the engine is a 3.1 liter Front wheel drive.
The thing is when you turn the key (not all the way on just far enough to roll up the windows) it makes humming sound that is coming from the rear end like where the fuel pump is. Sounds like a phone on virbrate and you can feel the vibration in the seat when sitting there, the sound don't last long and then it will stop when you try and start the car the battery has a strong charge it just won't start. It don't have no dragging sounds in the motor at all. It sounds like it would if it would be flooded, but it's not, it has plenty of gas in it. I am just really stumped on this one. I want to say it't the fuel pump but yet I don't. Also how hard is the fuel pump to take off if it is the fuel pump? Is the fuel pump located in the tank? The sound also sounds like a cow moaning if that makes any sense at all.
Thanks and any help would be greatly appriciated. Please do email me on this as well. Thanks again