We have a 99 Neon. When you turn the key there is a clicking sound under the hood, the lights and dings all turn on in the car but it wont start. Every now and then it will stop the clicking turn over and start...once its started it runs fine.

or might just be the battery. neons have a lot of trouble with any slightly loose wire.

I have a 2000 and the clicking is the starter jumping the silinoid. Yes you starter is going out, and it may be the next time you try to turn it over. Once it clicks, it goes fast.