I have a 1997 saturn and it will not start.

Try cleaning and tightening well the battery connections along with the battery wires to the solenoid and starter motor.

Bad connections and low voltage of 12 volts can result in this anomaly.

doubt it, maybe check ignition relay or starter solenoid

needs a new battery

Does the car make any noise when you turn it over? If it clicks when you turn the key the battery is dead. Quickest way to check a battery is to switch your high beam on. Get out and check the lights. If they are dim then the battery either needs charging or replacing.

How old is the starter? New or used?

IF STARTER FUSE AND RELAY OKAY.REPLACE THE NEGATIVE BATTERY CABLE COULD HAVE BAD GROUND AT CABLE.IF CABLE GOOD. I AM LOOKING AT FAULTY IGNITION SWITCH OR FAULTY TRANSMISSION SAFETY NEUTRAL SWITCH.

bad connections at the battery. This happened to my 1990 Oldsmobile Cutlass Calais. Had it towed to an electric shop thinking it needed a starter, battery, or alternator.

They cleaned the ends, and that fixed it.

I would start by rechecking the connections assuming the battery and starter are alright.

Wire brush until shiny as new.

Did you mean there is NO sound from the starter? The question says there is now sound from the starter. If it is a quick clicking noise, the new battery needs to be charged. Try getting a jump start for it or returning the battery, it should have come charged already. Not a good sign, these things sometimes bought new come with bad cells.

the ignition maybe bad are the car is not all the way in park also check the battery to make sure it has a good charge and it does not have a bad cell in it and the terminals are clean.

check the nuetral safety switch then check the starter

CHECK THE COILS, WE HAD THE SAME PROBLEM SPENT MONEY ON NEW STARTER, BATT, ETC. .....GOOD LUCK