1999 dodge neon just stopped running. The engine

it is possible that your neg battery terminal could be losing contact or coil could have stopped working and im sure the oil on the spark plugs has a bit to do with the running issue . You need to change the valve cover gasket make sure nothing is cracked clean up the valve cover and engine side surface install valve cover gaskets and bolts torque em down and see what happens youll probably have to replace the spark plugs or clean them up real good

Check the battery and the spark plug. Replace the spark plug if necessary.

Does the light work when you first turn the key? Does it come on? Check your ignition wires for arching also make sure you don't have a pool of oil in the spark plug tubes.

Be careful, when its running, slowly pull each spark plug wire up, if you see sparking coming out of the side of the spark plug boot, replace the wires and spark plugs. Use the correct Champion Spark Plugs.

Yes, very much so.

You can crank the engine over in drive? It sounds like a torque converter clutch that is locking up.

1. check ASD relay
2. check crank sensor, you may need to replace it

Good Luck

those neons are known for the coil pack on top of the valve cover to get cracked, if that is the case it will arc from the spark plug wires!!!
when it gets dark go out under the hood with a spray bottle full of water and while the engine is running spray a little water all around the coil pack and where the spark plug wires connect to the coil pack!
then while you are doing this, watch for any sparking/arcing you'll know it when you see it it will look like electricity kinda like a mini lightning bolt!!!
:-)

The timing may have jumped,Have the timing checked.

It still could be numerous other problems,so post back with details

Try shaking (gentle pull and push ) the wiring harness just below the intake hose on the drivers side of the engine! Then try starting it. let my known if it doesn't work
wilbecraft