Q: Car won't crank, dash lights do not come on, can't be jumped by booster pack.

The first time it died, I was driving at low speed and the engine cut out. When I tried to start it, the dash lights didn't come on as they normally do, radio and other lights worked fine. However 5 mins later it magically started. 2 days later, I was parked, car off, and had the same starting issue as before. But this time it didn't magically start. My friend was able to jump the car. Later on in the week, I had the same problem, but this time we could not get the car to jump start off my friends car. Tapped the starter, checked all the fuses of which were fine. Eventually it jump started after an hour of trying. Most recently, I drove 5 mins to the store and parked. I again had the same problem but this time was not able to jump it with a car or 3 different battery packs. Had to get it towed home. We've already replaced the alternator twice. The only thing that can get it started is an ac powered battery charger. But after it gets started, it's fine again for at least a couple days

My car has 120000 miles.
My car has an automatic transmission.