-Initally there was a code (P601), PCM will not communicate with scanner except for the one code.
-Started prodding around and ended up unpluging the crank sensor and cleaning the connector with break cleaner, plugged it back up, and the car started right up first try. I assumed the oil that had puddled up in the connector, shorted it out, and caused our problem. No such luck.
- The car ran fine for a while, and then again the thing randomly shut off while driving and wouldn't start back up.
-Unplugged the crank sensor, still clean, and plugged it back up, again, the car fired right up.
-Exact same thing happens again. Car runs fine for a while, then shuts off seemingly at random. Will not restart.
-Replaced crank sensor along with the leaky oil pressure switch, hoping that cutting off the oil leak source would stop problem.
-again car starts right up and runs for a while and another shut off with no re-start.
-replaced PCM. P601 code goes away, scanner can now communicate with PCM, and no codes, but still no start.
-unplugging the Crank sensor and pluging back in no longer works, and the car simply wont start at all.
-replaced coil. Still no start

any advice would be appreciated.

 

Check fuel pressure, Injector pulse, Spark, timing, and compression. Start with the basic and check back with the results.

 

I had the same problem. The PCM connector had many broken wires at the connector. I cleaned them up the best I could, clipped broken strands and got tape around them but there are a few that are only one or two strands. I am currently trying to find out the connector make so I can make a replacement. Rewiring the entire PCM circuit looks a bit daunting so I would rather replace the connector.
That is the problem with the Neon, front end is too low to clear parking bumpers. Wiring bundle gets rubbed against the parking bumpers and eventually breaks at the PCM connector.