Q: Won't turn over. No crank.

If the alternator quite working, this will mean the battery is likely discharged, which would be a normal condition when an alternator fails. The starting system uses ten times the current of every other electrical system on the car. It would be normal for the battery to be able to power the headlights, and still not turn the motor over with the starter. A trick that can be utilized is to watch the headlights while attempting to crank the motor. If the headlights dim, then the starter is at least attempting to crank the motor. In any case, it is prudent to first test the battery by load testing it. If i can carry half of its CCA (cold cranking amps) for fifteen seconds, the battery is good and there is another problem.

Since your alternator failed, I suggest charging the battery to see if that solves your problem. If not, then further diagnosis will be needed. You will need a wiring diagram and a test light to move forward with such a diagnosis. If you have the knowledge and access to the appropriate information, I would test your battery thoroughly and begin testing with a test light. The most common problem with a starting system problem is always related to high resistance or an open circuit. This often happens at the connection at the battery cable ends and batter post and at the starter connections.

Begin with the basics and check to see if the starter is recieving a signal from the key. If not, you will need to begin testing the primary circuit of the starting system.

If you require further assistance with this, I recommend the following inspection to help you out. Car is not starting

Good luck!