Why wont your 1985 Cavalier stay started?

The first thing that I would do is start the car and if you have time, diconnect the positive battery cable. If the car dies then it's the alt. Otherwise could be a fuel pump or possibly maybe in the trans. I had a similar problem in my 86 and it was the TCC, (torque converter clutch), which would not let my car idle right, and kill it. Hope this helps.