2002 Mercury Sable 3.0L VIN U OHV 185,000 miles

What's happening is that I'll put the key in and the lights, radio, headlights work just fine. But when I go to actually start the engine, I just hear a single click sound, and it sounds like it's coming from the starter, and that's it - the engine won't start. A few days ago, I tried jump starting the car and the first time I jumped it, it started up. The second time, it wouldn't start from the jump, so we took the jumper cables off, then a few minutes later I tried to turn on the car and it started up, but slowly (which led me to believe it might have been the starter). I have put in a refurb starter, new positive battery cable, and ignition coil, and none of that has worked. The battery is still good. Anyone have any ideas as to what the problem could be? Could it be the ignition switch, or maybe a relay switch? What about the cable that runs from the starter solenoid to the ignition switch? Thank you for your help!

 

A couple of things come to mind, what used to be known as the neutral safety switch and now is known as the MLPS manual lever position switch, and that has been changed to another name, located on the top of the trans could be making intermittent contact.
I believe there is a fuse for that circuit that might be worthy of looking at. You didn't mention the ground cable and related connections, how are they? Do you have any kind of anti theft system on the car? How about a coded key that might be getting tired?

 

How would I go about checking the neutral safety switch? I checked my fuses, and they all looked fine, but I'll go back in and check them again.

Regarding the ground cable, etc - Which ground cable are you referring to?

Also, I have the factory anti theft system on the car (the horn beeps one time after pressing the "Lock" button on my remote). And as far as the key, how would I be able to check to see if it is going bad?

Thank you for your help.

 

If you can do this, with a test lite connected to the starter solenoid terminal coming from the ignition switch. When you turn the key to the start position that test lite should lite and the starter should engage. If the lite, lites ,and the starter doesn't do anything the problem most likely is either in the supply to the starter , the starter itself or the engine ground cable. If the test lite doesn't lite when you turn the key to start , now you need to back track to where the signal was last.
If you were able to energize the solenoid at the starter directly bypassing all the safety features ,it should cause the starter to operate and crank over the engine. You need to be very careful to make sure the vehicle is in park because with the key on, it should start unless the anti-theft system could be keeping it possibly from starting.