Esteem 2000 - Electrical Problem. Maybe someone has an idea for me!!!!

Hello all!
 
I am new to this forum, and I just registered hoping someone could possibly have an answer to my problem.
 
I own a 2000 Esteem GLX with a 1.6L engine. I recently changed a faulty alternator, but there is still a bug. I explain:
 
Since I have changed the alternator, the low battery indicator on the dashboard is permanently lit. However, when I check, the alternator charges 14.1-14.2V at 2000RPM, which is well within parameters. And when the motor is off, the battery (which is brand new as well) gives me a 12.5V output, which is perfect. With motor on, even if I turn on the high beams, the heater fan, the rear defrost and the radio, I still get approx. 13V output, which is good.
 
I tought of the voltage regulator being faulty, but then again, I would get a output voltage too high.
 
If anybody has an idea, I'll be very thankful.
 
Cheers!