2002 Taurus won't start.

There is a starter solenoid on the passenger side fender well. It has 2 big threaded post and 1 or 2 small ones. Have someone turn the key and see if that is what's clicking. If it is take a big screwdriver and jump across the 2 big post and it should start right up

The click you are hearing is most likely the start slenoid making contact, however you should short the large wires @ the solenoid to make certain the starter still doesn't run, if so try tapping the starter with a hammer to shift the comutator a litle and try to start. Even if it now starts the starter will continue to give you problems so the proper fix is change the starter

You have a wire going into your starter in the opposite side of the starter. There should be 2 poles where you connect wires. The only one that goes to one pole is the heavy gauge wire coming from your solenoid

I am guessing that you already suspect the starter motor. If the battery is fully charged and the car won't crank over that could be the problem. You could try jumping across the starter solenoid first, if you can get to it and see if maybe it is just the solenoid. You could take the starter to a place like AutoZone and they can test it for you.

Ignition problem... No signal from ignition to solenoid...run a starter draw test to confirm starter is ok --- You can run your jump wires to a remote starter button or switch to get around it for now.

I hope this helps.

When the bushes in a starter get worn, it can cause the armature to rub on the magnetic poles (poleing) This can cause the starter turn slow or not at all
The sintered metal bushes are like bearings. Not to be confused with carbon brushes which are the electrical connectors.
When a starter clicks, it is the solenoid you can hear.supplying power through the brushes.

A starter that is poleing,often stops in a place where it isnt rubbing, and works fine the next start.
There can be other problems with a starter , perhaps one of the brushes is sticking, or the solenoid.
When it happens a tap with a hammer on the starter or solenoid, while a friend turns the key, is enough to get it working( this isnt a fix but might get you started in an emergency)

There is also the possibility of a loose or dirty cable connection, from when the new battery was installed

Could be the starter solenoid. Locate the starter in your car, and have someone turn the key for you while you take a hammer or screwdriver and lightly tap on the solenoid on the side of the starter. If that doesn't work, take the screwdriver and lay it across the 2 terminals on the solenoid at the same time with someone turning the key. But I must emphasize, BE CAREFUL, as the screwdriver could be welded to the terminals in a split second. You won't get shocked or anything like that, but there is alot of juice there.

Ignition may be bad or stater/solenoid. Try "jumping" the starter with the key in the on position across the poles with a screwdriver if it turns over its most likely the ignition switch. If it just clicks its the starter itself. Or a little of both.

probably dirty connection on the battery.The headlights should come on bright, then dim only slightly when the starter engages.
Remove the battery cables and clean all corrosion off the terminals and connectors. The lead must be bright and shiny to make a good connection. Once you have checked and fixed the battery connections, and still no crank, find the starter relay and tap it firmly ,then try again. Still no crank, manually jump across the relay to 'force' current to the starter solenoid. Still no crank--replace the solenoid

Check the starter. Sounds like it is not getting any juice. Tap on it with a long metal pole or hammer while someone tries to start it.