How can you tell if it is the alternator on a 1999 dodge neon if lights and radio turn on but won't start?

The alternator is in the car for two purposes. One ... to charge the battery. Two ... to run anything and everything electrical within the car when it's running. So basically, the battery is only there to start the car and that's it, the alternator has nothing to do with the starting of the vehicle.

If the car won't start, it's probably NOT the alternator. It's a possible problem with the battery or within the starting system. It could be caused by something as simple as making sure the shifter is in the park position all the way. (automatic transmission only of course) If this is an automatic, you can also try placing the car in neutral but MAKE SURE YOU USE THE BRAKES OR PUT THE EMERGENCY BRAKE ON before and while starting it. If it starts in neutral but not in park, it's the neutral safety switch gone bad.

If the car is a manual, the clutch safety switch located (usually) above the clutch pedal may be the culprit.

Now ... there are many things in the starting system that can go wrong from a fuse, to a starter solenoid, a starter relay, the starter itself, the ignition switch, a bad connection somewhere, a broken wire or a security system within the car. There are other things that can go wrong, but without knowing the year make and model of the vehicle, this is the best I can do for ya. Good Luck!