Wow! You really need some punctuation in that huge sentence. It can be read a pile of different ways:
"I have replaced the starter and the alternator already and I still hear the click when I turn the ignition"
"when I turn the ignition all I hear is a click and the lights don't stay on when I turn the ignition"
Which lights are you referring to? Head lights? Dash warning lights? Interior dome light?
Also, in the future, you should start a new question. When you piggyback on someone else's, we are the only two people who will see it and be able to respond. That does you a disservice because one of the other experts may know exactly what it will take to solve a problem but will never see your post. Also, people researching a previous solution might not read all the way to it when the first post doesn't relate.
In this case, I'm not a Cadillac expert but I am a starter system specialist so I can give you some steps to get started. Find the starter relay under the hood. There's going to be four wires on it, and two will be fatter than the other two. You can back-probe under the connector or you can unplug the relay and go right on the terminals in the socket.
It just occurred to me that I may be getting too far ahead. GM is famous for using the larger starter terminal as a tie point for all the car's other circuits. They attach fuse link wires there that turn into regular wires within a few inches of that terminal. You can have nothing more than a bad cable connection. That will cause a drop in voltage when you try to activate the starter, and that "voltage drop" will affect the other circuits and cause lights to get dim or go out.
A bad battery can do this too, but with GM's side-post battery cable disaster, bad connections are a lot more common. The place to start is by using a test light or voltmeter to measure the voltage right at the starter. Place the ground lead right on a paint-free surface of the engine block. Put the positive probe right on the large copper stud on the starter. You may want to find some clip leads to connect the probes so you don't have to hold them during the test.
Be sure the positive probe is on that copper stud, not the cable terminal that's attached to it. You'll find full battery voltage which will be 12.6 volts if it's fully-charged. The issue now is what does that voltage drop to when a helper tries to crank the engine? It must stay above 9.6 volts. With a bad connection, it will be pretty obvious because you'll find just two or three volts, if that. Depending on what you find, and when you clarify the description of the symptoms, we'll figure out where to go next.
Saturday, August 16th, 2014 AT 8:47 PM