Sounds like the starter may be failing/maybe just the teeth/maybe the Bendix (the part that throws the starter teeth into the flywheel).
Even worse, the flywheel teeth may be worn.
Let's hope not!
You may pull the starter and look at the teeth, also have it tested at a popular auto parts store. Sometimes an intermittent problem with it throwing in might be hard to detect.
If it comes down to replacement, maybe this will help you.
https://www.2carpros.com/questions/2001-dodge-neon-milage-just-want-put-fliuds-their-locations
Keep us posted.
The Medic
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Tuesday, October 3rd, 2017 AT 8:43 PM