Faulty wiring, faulty ignition switch, or possibly a faulty neutral safety switch.
A solenoid is a type of magnetic switch responsible for helping your starter motor turn on the engine. When the solenoid sticks, the ignition struggles to start. When this happens, usually your key will "catch" in when you turn it to start the vehicle.
Did you replace the ignition switch? Not the key tumbler but the actual ignition switch. If so, you have a wiring problem.
Solenoid could be installed incorrectly. Could be electrical connection on the solenoid. Did you re-connect the battery? Could be a bad starter motor...or a stuck starter motor. Sometimes a light tap or two on the starter motor (not the solenoid) with a hammer will free it up.
If you can hear your starter motor turning but not the engine you have some teeth missing on the ring gear. If you can hear nothing, not even the starter motor solenoid clicking into place, you have a connection problem between ignition switch and starter motor.
the solenoid itself is probably bad, if not that probably the ignition switch I agree 100%, check the solenoid first then the switch.
looks like the starter motor. the clicking sound appears to be the solenoid on the starter motor. when you turn the ignition, the solenoid click and its supposed to make contact to the motor. if the contacts are dirty, then the car won't start. repeated clicking will eventually make a little contact allowing the motor to turn. try changing the starter motor or servicing it. you can do it urself. remove the motor and pull the solenoid out. clean the brass contacts. they should be under the connections where the wire from ur battery connects. if it seems to be too much work, just get the motor replaced.
Not to bash on the last answer, but, the starter solenoid probably isn't at fault here. If it will start with the screwdriver then the starter solenoid is functioning. It either does or it doesnt. The answer lies in circuitry back from the solenoid to the ignition switch. You could have a bad ignition switch or neutral/safety switch.AnswerDefective starter solenoid.
When opened by the starter switch, it sends electricity from the battery to the starter motor to start the car.
The clicking noise you can hear is the starter solenoid clicking into place. If the starter motor does not turn the engine immediately, it is probably the best place to look. it sounds like the starter motor is faulty.
Possible bad starter motor or solenoid. Possible locked up motor (did you run it out of oil?) Possible bad ignition switch. Check all the fuses with a test light.
Check the neutral safety switch,it is located on the transmission or on the steering column ,under the dash.
The most likely explanation is that the solenoid itself has failed. The next most likely explanation is that the wiring to the ignition solenoid is not making proper contact or there's a bad ground connection. The least likely explanation is that the electronics that control the ignition solenoid (MPEM or whatever it's called on your model) is broken.