non-starting '83

My Imperial's little sister has conked out, in about the worst possible place. I put my '83 Cordoba in the underground apartment garage I use to store the Imperial and Riviera, when I took the Riv to Chicago on a road trip last week. When I returned on Monday, the Cordoba wouldn't start. The lights, radio, clock, windows, etc. work fine. When I turn the key there's one click, and no other life. It doesn't try to turn over at all. I tried jump starting it with the Riv, and with a charger box that a friend has, and tried in park and in neutral. I moved the shift lever back and forth too. Nada. The car has 156,000 miles, and the battery is exactly 5 years old. It has given no indication it's failing, and if it was, then why do the lights work? I suspect the starter, but have also heard from friends that it could be a ballast resistor or a neutral safety switch, which I had to replace in the Imperial two months ago. Do I have these in this car, with a 318 cid v-8?

Trying to get the Cordoba out of the garage will be a real b**ch, with a curving driveway up an incline, and a couple of turns and forward/reverses to get it out. She's my daily driver, and I really have to stop using the classic, show-car Riviera for commuting. Any thoughts, guys and gals?