BMW Repair: 1984 318i automatic, battery drain, alternator

Question
My car will only crank with a hot or freshly charged battery. I've changed the alternator had it tested and everything its fine. When the car gets to the point where it won't crank, I can get a jump but it lasts maybe 20 min, but nothing electrical will work. If I try to turn on the lights after a jump it'll try to die. If I open the door it'll die, but the radio won't come on. My vin # is wbaak8401e8776179. Thank you in advance.

Answer
I have thought it over and then it hit me. Its a 1984 318,question..does the battery light come on when you turn your key to the on position?If the bulb does not light then it needs to be replaced as it WILL NOT charge without the bulb.Which in turn will cause all of your seeming like battery drain issues.