Reinstalled starter and ignition wont turn over

if your saying your starter stays engaged after starting engine till you cycle thru the gears , your starter needs serviced , most likely a worn bendix pivot bushing

two options 4 repair
1= replace starter
2= remove starter and have it professionally rebuilt then reinstall it

Is this a no crank, no start issue? Or is it a crank, but no start issue? If no crank no start, when turning the ignition key to the start position, and you get no cranking, then you have a couple possibilities...
bad starter, bad solenoid at starter, or bad Battery connections.
It could even be a bad positive battery cable. Bad battery terminal connections, are the most common result of a no crank no start issue. Check the terminals, clean them, clean them, and did I say clean them?

check this... Turn the key to the on position just in front of the start position. Then turn the lights on, are your headlights on. If they are on, that means you' are getting power through the ignition system. So ignition switch is not problem.
There is also a circuit breaker in the under the dash fuse box. It runs your power for the ignition system. It's a small half inch by 1 inch? Silver block. Try replacing that?

The crank sensor only comes into play while the engine is cranking or running to tell the computer where TDC is.
A no crank issue would be only the starting or security system.
Do you have battery power at the starter when the key is in the start position ? Are the battery cables clean and tight on both ends ?

If the starter turns but does not turn the engine over, you can do a couple minor things to check why. Pull the starter off, have it checked at an Auto Parts Store, like O'Riley, which does the tests free, and see if the starter has had a pin sheared in the Bendix, or if it does not spin the bendix out. If this is the case, just buy a new starter, and get the lifetime warranty.

If the Starter does work fine and spins properly, sending the bendix out, then check the flywheel before reinstalling the starter. You may have shed some teeth, or something came loose.

After these checkups, if everything is working properly, then check the distributor when cranking the Starter, to see if it is spinning. You will need remove the Distributor cap to watch it. You can also, while the starter is off, turn the flywheel with a wrench, or screwdriver/bar, whatever you can use, and see if that turns the engine over at all. You may need remove a sparkplug to release the compression to do this.

If all this fails, then there is something inside the engine either broken, or disconnected. Check to make sure you are getting spark to the plugs.

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If the engine doesn't turn over it is not a fuel issues as fuel will keep it from starting. However the engine will still turn over what is more likely is a starting system concern since it just clicks it is probably the starter or starter circuit. again the fuel pump cut off only turns off power to pump which will cut fuel.. engine will still crank.

Replace your starter.

sounds like you have a bendix and ring gear problem, sounds like you have a starter bendix engagement and disengagement problem, drop starter and inspect the flywheel ring gear and starter drive gear (Bendix) .

Look for worn teeth on the flywheel it only will happen in one or two spots 180 degrees apart cause the motor always will stop in one two places... seen it a 1000 times...

Also your ignition switch could be sticking in the start position. common problem. If it stops when you put the car in drive or reverse gears then its something with your ignition switch.