1989 Nissan Maxima battery, starter, alternator

I started having trouble starting my car and diagnosed the problem to be a weak/dead battery. The head, inside, heating, etc worked, but with alot less power. Got the battery tested they said it was dead, so I bought a new one. Put the new battery in and the car worked fine. Tried starting the car up the next day and it didnt even turn. The car was completely dead, lights, radio, heating, etc. So i tested the battery, and read that it was fully charged. So now I dont know if there is a problem with a fuse, the starter, or even the alternator.