2001s10 starter won't engage makes no noise everything else works changed the ignitions switch could it be the neutral switch . I you play with the key sometimes it well start

time for a new starter

This could be a couple different things causing your No-start condition. first thing I would check (Battery is good) access the starter solenoid, the small single wire connection is the start signal. Test for 12 volts here with DVOM or test light while someone turns the key. If there is 12 volts reading, the starter solenoid is defective. If there isn't 12 volts reading check all the fuses (with test light).
The second item causing the trouble could be the Neutral Safety Switch (Auto Trans) or Clutch Safety Switch (Manuel Trans) These could be open or out of adjustment.
Hope this helps you...

The ignition switch sends voltage to the starter solenoid, if no neutral or brake switch is involved. It is sometimes located ON the starter. It activates a high-current switch that engages the starter. If you don't hear a click, the solenoid could be bad. Since the high current can damage the contacts, you could still hear a click and not get the starter to spin. Sometimes hitting the solenoid, or starter lightly with a wrench or hammer will realign the contacts and you can get another spin from the starter. Hitting the exposed contact on the cable that goes straight from the battery to the solenoid can cause a spark, or explode the battery.

So, the ignition switch, battery, starter, starter solenoid, a fuse, a neutral switch, brake switch, or wiring can be the cause of a starter not engaging.

might be a burned spot on the starter contacts where the brushes power the motor.
tap the starter to see if problem goes away.
sometimes you can clean the contacts but that is a temporary fix.

The ignition start circuit is the path from the ignition key in cranking mode to the solenoid on the starter. The path travels through a starter relay and a neutral safety switch before it reaches the starter.
This must be the circuit not working on your car.Make sure battery and starter connections are tight.Check for power at the starter solenoid terminal with a testlight when someone turns key to crank. If you have power there, they sold you a defective starter. If you have no power there then it could be the relay or the neutral safety switch.

The keyswitch is linked to the neutral safety switch. The neutral safety switch is the part that makes the starter work only in Park and Neutral.

Think of the Neutral switch being at the bottom of the steering column; and the Ignition switch is at the top. Any play between these two points will not move the Neutral switch far enough to engage. The Gearshift on the floor is tied into the system just as if it were a column shifter.

I would suggest a trip to Autozone or Oreilly for a Neutral switch. The parts people can show you diagrams and locations for it. The Electric parts for this are Plug and Play, just a plug to take off and reinstall on the new part. Since it worked when you shook the Gearshift, chances are the looseness is where the Neutral switch meets the shift mechanism.

It's most likely the neutral safety switch. Try putting the shifter in Neutral and slipping it just a little toward Park and see if it'll crank. If it does the neutral safety switch is the problem but worn linkage is the cause.
You've already check or replace everything else so it has to be this or the ignition switch.

Check the neutral safety switch,and then the ignition switch.

Help please....I have Mazda Protege 2002...the car was driving good..and suddenly the car didn't start at all i changed the starter the battery is fine because when i start the car the lights comes on and the radio works. I don't know what is the problem is...when i start the car it makes noise of tik tik. Please help me????

sounds like a dead s wire to the starter if you can jump it across thers no power to s wire