While it’s difficult to diagnose a car problem from a distance, if your 2005 Dodge Neon won’t start and doesn’t click, it could be a problem with the starter solenoid. A starter solenoid is a part of an electromagnet that engages the starter, so if it’s faulty, your car obviously isn’t going to start. When the solenoid goes bad, you won’t hear the click that you would normally hear if you had a problem with your ignition switch or battery.
The only surefire way to diagnose the problem is by taking your car to a mechanic. If the starter solenoid is indeed the issue, you should reasonably expect to pay between $375 and $450 to repair it.