The car will not rev over 3,000 RPMs.
Fault codes need to be read out of the engine computer to guide the direction of diagnosis. If no fault codes are stored, then possible issues could be a camshaft sensor, or crankshaft sensor that losses its signal at that engine speed. Also, the engine management system on the Neon Turbo uses a speed density system, which uses intake manifold pressure to set up injection timing. If the MAP sensor is not reading pressure correctly, then injection timing may not be set correctly by the engine computer.
One last thing to check is fuel pressure and volume. If the fuel pressure is dropping as engine load increases, then the engine will stumble due to a lack of fuel.
There is a technical service bulletin on the Neon for updated spark plug wires, but this issue doesn't just limit the engine RPM's to 3000. Nevertheless, you may want to make sure that you have the updated wires. You may want to enlist the help of a mechanic, such as one from YourMechanic, who will have the equipment and expertise to diagnose these types of drivability issues.
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