95 sentra alternator?

Hi, I'm hoping someone can help me with a repair problem. I have a 1995 Sentra and my battery light and brake light were on for a few months. I was told by a dealership that my alternator was bad about a month ago. Over the past few days, it was getting harder to start so I decided it was time to get the alternator. I intstalled it and the warning lights are now off, but it won't start. I tried about three batteries and it would start the first go with a battery and maybe the second, but not a third. Did I get a bad alternator? Did I install the ground on the alternator wrong? Maybe the starter is bad too? I'm perplexed. Any insight would be greatly appreciated.
Puukki