I don't know what is wrong with your car, no one does. We don't know the history or symptoms, we only know what little you have posted.
But the above sentence CANNOT be overlooked. This is a MAJOR clue to what is going on.

Go into much more detail. Try answering this:

You yank the cable off and leave it off. Then you put it back on.
EXACTLY what will happen if you then try to start the car? Be wordy. Can you start it and go into town and go shopping? Or can you start it but it dies right away?
Are you REALLY saying that if you remove hte cable and put it back on, you can start the car and drive it - but you can't shut it off and restart it unless you disconnect the battery?

Because that is what you just said - now we need to know: Is that what you REALLY meant to say?