trouble starting

Before I turn the key all the way I usually hear the pump run for a 2-3 seconds
and then stops.  I then turn the key all the way and the car starts.  When i do
not hear the pump run the car will not start, yet turns over a mile a minute.  
Happens every so often.   Once i had it towed to the shop and for not starting
yet it worked every time for them.  What is it?