The idea that it won't engage leads me to believe there could be an issue with the flywheel. You need to remove the starter and check the flywheel. However, before doing that, record the sound it makes when the starter is engaged. I need to hear what it's doing to make sure it is a problem with the starter system and not something other.
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Here are directions for removal and replacement of the starter. The attached picture correlate with the directions (actually are the directions).
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2001 Mitsubishi Eclipse RS L4-2350cc 2.4L SOHC MFI
Removal and Installation
Vehicle Starting and Charging Starting System Starter Motor Service and Repair Removal and Replacement Removal and Installation
REMOVAL AND INSTALLATION
Starter Motor Assembly
see pic 1
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Again, I need to hear what it is doing. You may have a broken timing belt which could allow the engine to turn really fast.
Let me know.
Joe
Image (Click to make bigger)
Thursday, January 9th, 2020 AT 5:52 PM