I have a no spark situation at the 1st and 4th coil on my 97 Plymouth Neon.I notice the wires at the cam shaft position sensor was melted and the wires were touching.I replaced sensor and connector wires and still no spark.I then disconnected the middle wire on connector and began to get spark but still no start.This is 4 cylinder engin

Could be the coil, or a crank or cam sensor.
The components would need to be tested.

If there is spark to cylinders 2 & 3 than it is not the cranks sensor. Cylinder 1 & 4 are on the same coil and cylinders 2 & 3 are on the other coil. Replacing lithe coil pack will likely solve you lack of spark on cylinders 1 & 4.

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If its not getting spark the choices are limited. You already replaced the coil pack so whats left is ignition module, crank sensor, knock sensor, cam sensor, or the timing was not was not set properly when putting it back together. Any one of those would create a no spark situation.

Have the alternator checked,it is most likely shorting out,or discharging.

It could be the Crankshaft Position Sensor, if you want another guess.

do you have fuel,spark, and injector pulse? if not cam or crank sensor

YOU NEED TO CHECK DARK GREEN/ORANGE WIRE AT IGNITION COIL WHEN CRANKING ENGINE FOR POWER..IF NO POWER,SHUTDOWN RELAY IS NOT BEING ENERGIZED..THIS ENGINE ALSO HAS CAMSHAFT POSITION SENSOR ON END OF CYLINDER HEAD..ENGINE CONTROLLER NEEDS CAM AND CRANK SIGNALS TO ENERGIZE THE SHUTDOWN RELAY..UNPLUG CRANK SENSOR AND CHECK VOLTAGE ON ORANGE WIRE..SHOULD HAVE APPROX 8V..IF NOT..UNPLUG CAM SENSOR AND SEE IF 8V SUPPLY RETURNS..IF NO POWER TRY UNPLUGGING VEHICLE SPEED SENSOR LOCATED IN TRANS HOUSING WHERE RIGHT SIDE AXLE COMES OUT OF TRANS..IF 8V RETURNS..THE SPEED SENSOR IS SHORTED INTERNALLY..THESE 3 SENSORS SHARE THE SAME 8V SUPPLY CIRCUIT..WITH SPEED SENSOR UNPLUGGED,PLUG CRANK SENSOR BACK IN AND TRY TO START ENGINE..HAVE SEEN THIS SAME PROBLEM AT WORK RECENTLY

you have a bad crankshaft sensor. replace the crank sensor.

dodges and gm's are known for this problem.

check the asd relay

This link is to the ignition section of the factory service manual.
NEON IGNITION