What could problem be?

I was driving at night about 45 mph and when I went to accelerate the car did not, slowed down to idle speed. I pulled over and put car in neutral and engine reved up when I accelerated. Put in gear and car would not accelerate was able to travel about 2 miles and car engine killed and battery appeared to be dead. Car would not re-start. I did not get an alternator warning light prior or at any time. I took it to a mechanic and they said it was the alternator. They replaced it and charged the battery. I picked up car and drove 15 miles and the same thing happened. Was able to drive at 5 to 10 miles per hour for about 2 miles and engine killed. The car sat idle for 2 days and I was able to start the engine without charging the battery. The battery is a Sears Die hard and appx 2 months old. Somehow I feel that the alternator was not really the problem to start with?

Thanks, Help,
glen