My 2001 Mercury Sable that won't start from time to time.Any ideas?

My 2001 Mercury Sable that won't start from time to time. Dashboard lights come on
and chime sounds (sounds same as when door is left open). Engine does not crank.
After trying several times and sometimes waiting for 15 minutes or so, engine will start
right up. Have brought the car to 2 mechanics as well as the dealer. All said every time
they tried to start the car, it fired up right away. Drove the car yesterday and made 4
stops. The car would not start the 4th time. Had to wait and try several times before it
started.