1997 Dodge Neon Will not start

Your gonna have to check the spark and the fuel after the vehicle has warmed up to see if you can catch it acting up, I mean it could be several things, when its cold it will be fine but when its hot, some circuits may stay open or closed and not work properly. Also you may want to check the mass airflow sensor and the engine coolant temp. Sensor. Usually the engine light will come on when these two are bad, but at this point it looks like the problem is intermittent thus causing the engine light not to illuminate. I'll send you a couple of video links that show you the easy way to check your spark and fuel. Then we can take it from there.

http://www.2carpros.com/car_repair_video/test_fuel_injection_pressure.htm

http://www.2carpros.com/car_repair_video/test_engine_ignition_system.htm