Car shut off while driving will not start

I have the car listed above 4 door sedan.
Car shut off on my way to work going 65 mph. Just shut down. I steered my car over to the side of the road put it in park turned my key to its off position waited a few seconds and went to start it and when key hits the start position it makes a high pitched whining/buzzing sound, but will not start up. Had to get it towed back to my place.
When I turn the key to its on position all lights work fine and do not dim when I try to start it.
I just need some help suggestions or anything pointing me in the right direction to get my car running again. Please so I don't have to spend a whole lot of money getting parts and switching parts that really don't need it and it ends up not being the problem. Thank you