I don't know which of the hundreds of people on this site answered the question about the crankshaft sensor. When you post a question on this site; it is seen by everyone here, and there is no way of us knowing who you intended it for; unless you noted the name on the logo by the answer you saw, and include that name in your request.
Your mention of the "engine not turning over all the way" is confusing to a mechanic. Many non technical people do not clearly explain the symptoms of a starting problem; and when that happens; we can't be of much help, until the confusion is cleared up. The literal meaning of an engine not turning over all the way is that the starter turns the crankshaft a certain distance (typically less than one revolution) but it then jams and will not turn further. This is not a common symptom; but it can and does sometimes happen. The usual cause would be ignition timing which is way too far advanced, an overheated engine, or a discharged or borderline weak battery
If the engine doesn't start because the starter doesn't spin freely; and
the crankshaft seems to be jammed or locked up; this could be caused by
a broken timing belt on a car that has an interference type engine; or a
head gasket that blew and filled a cylinder with coolant. Your 2002 Neon has an interference engine; which means that; if the timing belt breaks or stretches from age and then jumps out of synch with the crankshaft; the valves will collide with the pistons; which often jams the engine and prevents it from turning freely. The damage thus caused often exceeds the value of the car. This catastrophic problem can be avoided if people read and follow the manufacturer's maintenance schedule; in which the timing belt typically should be replaced at 60,000 to 90,000 mile intervals. But some people don't know about this, and don't even bother to find out whether there are any critical things which must be done to their car to avoid disaster. Most cars has a timing belt or timing chain; which must be replaced at some point.
Unfortunately; all too many people describe a situation where the starter turns the motor freely; but the motor doesn't fire and begin running on its own; as "not cranking" or possibly "not turning over all the way." This is not what is happening in those situations: The accurate description of this phenomenon is that the motor cranks freely but the spark plugs do not ignite the fuel in the cylinders; so it doesn't start running on its own.
I usually answer more questions with a crank position sensor solution than most of the other people here. Sure; replacing the crankshaft position sensor can solve a starting problem; but only if the problem comes from there not being any spark.
If the car doesn't start when fuel is being pumped up to the engine; but is not being injected into the cylinders; the part that addresses that problem is called the camshaft position sensor.
And it the starting problem is caused by no fuel reaching the engine's fuel rail; that would be caused by a failed fuel pump; or a clogged fuel filter, or a bad fuel pump relay, or a tripped fuel pump inertia switch, or on some GM cars, a bad oil pressure switch or a bad fuel pump wiring harness.
If the starter spins faster than it normally does; but the engine does not start; this would usually be caused by a broken timing belt or a timing belt that has jumped out of synch; on a non interference engine.
In order for an engine to start and run; it must have spark, and that spark must occur at the right time. It must have compression in the cylinders. And it must have fuel going into the cylinders.
You can check for spark by disconnecting one plug wire, and connecting a spark spark plug to the end of the wire, and clamping the plug body so that it presses against a metal part on the engine; or a inserting a bolt that snugly fits in the wire terminal and holding the wire well back from the end; with the end of the bolt a quarter or a half inch away from a grounded metal part on the engine. Have someone crank the starter while you watch for spark at the plug or the bolt.
If you have a spark; a crank position sensor will not solve the problem.
You can check for fuel by spraying a 2 second burst of engine starting fluid, or pouring about 4 ounces of gasoline into the throttle body air inlet; quickly reconnecting the air duct hose, and trying to start the motor. If it fires or starts briefly and then stalls; the problem is lack of fuel.
If it is not a spark or fuel problem; it often turns out to be a compression problem; which is most commonly caused by a bad timing belt.
If you want do discuss this further; please click the "answer this question" button under this response, type your message in the box that appears; and click the "submit answer" button. I'll try to get back to you soon.