Just to wrap this up.
I bought the new alternator for about $190 (minus $45 for core.) I got up early in the morning and disconnected the battery and was getting ready to get under the car for another couple of hours of struggle to get the old alternator and put the the new one in. I had driven the car with the new battery to Kragen and they were able to hook it up and told me that the alternator was not putting out anything. Just before I was about to start the job, it occured to me to look at the fuses in the engine compartment and discovered that there was a 75A fuse for the alternator. I knew these existed but never knew there was one for the alternator. Pulled it out and of course Kragen does not carry this kind, so I went to the Nissan dealer. I got a new one for $30 and the guy confirmed that it was bad. I replaced it and this was the problem. I took the alternator back and got my $190 back. Problem solved.
The question is why did it happen? Well, it just happens that maybe a couple of weeks prior, I had to jump start the car and I'm pretty sure I hook it up wrong (trying to rush.) The cover that goes on top of the battery covered the signs on the posts. Dumb thing to do, but I learned my lesson. Thanks everyone for your input. I did end up replacing all the belts which were in pretty bad shape.
