Maybe try changing your battery cables at starter and engine block ground connection.
If the starter is clicking, that's a good sign. Replace the battery and make sure you didn't have a drain on it. This problem could be caused by several things, but a weak battery or bad starter solenoid would be at the top of my list of things to check.
Your problem is the starter solenoid. It may be a remote solenoid mounted on the inner fender well. You can easily check it by running a battery booster cable from the positive battery post to the starter side of the solenoid wiring (the heavy wiring). If the starter operates, the solenoid is bad.
These answers by mechanics about dead batteries are amazing me. I am a girl...really into cars because I have had a few. I just had this problem in my 1989 classic Saab. The problem is your starter...The clicking sound means that the pin inside of the starter is not projecting itself and thats why when you turn your key you hear a clicking. Get your starter tested
Check battery cables for looseness or corrosion, also starter solenoid Also Neutral safety switch Had this problem and went through everything, finally had dealer replace the PCM and it was fixed. Cost was about $600 parts and labor.
If you're certain the battery is up, and the engine runs normally after you bypass the solenoid, you need to find out which part has failed. Check the solenoid first, then the keyswitch, and finally make sure the neutral lockout is functioning properly.
This happen with my 2000 Alero. I finally found a small damp spot on the fuel injection solenoid. I had the solenoid replaced and that fixed the problem.
If the check engine light is or has illuminated, check for codes.
by clicking the 1st one,then the 3rd one, and finally the 4th one
by clicking forward ten times then backwards and finally reaching the yellow rainbow where the magic box will appear
You probably need the original key fob for the car. This is regardless if you have an alarm for the car. I've changed the battery twice in the last five years for my 97 Villager and each time I've had to "reset" the "alarm" via the key fob. The last time, I had to uncable the battery twice because it would not "reset" using the key fob before finally accepting the "unlock/disarm" from the key fob.
Check the battery mine 1995 Z71 did the same thing changed starter still did same thing finally was told to check the battery after it sets awhile battery does not have enough juice too kick the starter in I had battery checked sure enough on cell on battery was dead bought new one not a problem since.
For 4 Cyl.: Start by disconnecting the neg. battery cable from battery. Then remove the heat shield clamp and shield (if equipped). If OHC model, then the air pump tube needs to be loosened at the exhaust manifold and the bracket swivelled clear of the starter as well as removing the exhaust pipe bracket from the tranny bellhousing. Disconnect the battery cable from the starter and the solenoid wire from the starter solenoid. Now remove the bolts attaching the starter to the bellhousing or block. Finally, remove the starter. Note: some OHC models have a shim between the starter and the block, don't lose it and don't forget to reinstall it when starter is replaced. Starter installation is the reverse of removal. For V6/V8: Start by disconnecting the neg. battery cable from the battery. Then undo the steering shaft coupling from the steering gear (mark the relationship of the steering shaft to the steering gear input shaft and unbolt or remove the rollpin from the coupling) and move it out of the way. Remove the starter mounting bolts. Finally, remove the starter by moving it forward and lifting up and out. Starter installation is the reverse of removal.