My alternator went bad and I brought it to a.

My alternator went bad and I brought it to a mechanic and it was fixed. I also replaced the battery with a new one however the battery light is still coming on and it stays on permanently. When I try to start the car, I have a problem starting it. The battery life has even enough power to turn on interior lights and dash board lights but not to start the car. The battery light is still on. What could cause this problem? Is it that the alternator is still not charging properly? Is there a short somewhere? What could it be?