The car will not start up, yet when the battery is hooked up the headlights come on. Nothing else t
Sounds like bad starter or starter solenoid, or perhaps the battery is just live enough to turn the headlights on, which I have seen happen.
Pull the battery and have it tested at your local parts store, if you can't test it yourself. If it is good then most likely the starter is shot. Usually the starter will click once if it is getting power and is seized. You can also try hitting the starter with a hammer, then try and start it, sometimes it works. But that would mean that you need a starter, not that you fixed the problem.