1997 Chrysler Sebring Car sometimes does not start

The car will turn over and start in the morning and will continue to work if only driving a few miles however if you drive for more than a few miles and turn off the car and attempt to turn it back on then you will only hear the fuel pump turn on but there is no click from the solenoid and therefore the car does not turn over. I have determined that the problem is not the starter because of this due to the fact that the car does turn on at random times during the day, mostly the morning for some reason, however the car at some times, of course when we need it the most, will not turn on. What could our problem possibly be?