When the ignition switch is placed in the start position the starter spins at a high rate of speed, centrifugal force moves the spring loaded bendix forward and engages the ring gear teeth which turns the engine to initiate the start.
Usually the first indication of a malfunction is when you attempt to start the engine, the starter spins with no load and sounds like an electric motor running (which it is). When this happens the bendix spring or retainer washer on the end has usually broken.
I'm not sure if you can buy just a replacement bendix or not.
What the Addict said, except before you start buying. Remove the starter and clean the end where the gear and spring are. It may be as simple as some crud in there that is holding up the engagement. After cleaning it, you can hook the power back on and see if it engages.
bendix is a good start.
you said the starter is spinning you didn't mention a grinding or squealing noise.
so your bendix isn't engaging the ring gear. this is caused by dirt, binding/malfunctioniing bendix, or not enough speed from starter(low battery, faulty wiring, or bad brushes/ armature). usually if the spring breaks the bendix won't retract.
first thing as said ^^ clean the crude out of the bendix. make sure the bendix is free. if it still won't engage take the starter off, and hook up jumper cables to a good 12 volt battery(car battery is fine) hook the positive on the nut(not the stud) and bump the body of the starter with the ground. if this throws your bendix you can bet its a battery or wiring issue. if not you probably have bad brushes or armature. your dealer can rebuild your starter, or i could tell you how.
let us know how it turns out.
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