Why is my Battery Light always ON although I put a new battery? HELP!

Hi everyone!

I recently bought 2006 Honda Inspire (Accord) 3.0 V6 automatic. I noticed that my Battery Light has been on recently. In addition, the system monitor sends me message that there is no charging. I watched many YouTube videos, checked by using multimeter both the battery & the alternator, with the engine on & being shut. My battery voltage is 12.7V (above 12.6V), whereas with engine on it is 14.22V (14.2V - 14.7V should be optimal). I also did the “Load Test”, with headlights, fog-lights, hazard-lights, radio, cabin-lights, rear-defroster, wipers, and AC (fan-blow put to max) being turned on and the voltage dropped to 12.4V. Interestingly, if I turn all of these appliances except the AC on, the voltage keeps above 13V. As soon as I turn the AC on, especially immediately after one of the two fans start working, the voltage drops to 12.4V, as I mentioned previously. In addition, I also checked the voltage drop from the alternator, for both plus and minus terminals of my battery. In both cases it showed a relatively stable -.06 / -.07V (both during idling and with 2000 rpms). Eventually, after checking my battery at the gas-station once again, I decided to replace it with the new one, although I’m not sure that the old one was bad. However, the Battery Light on the dashboard is still on, together with the system message that the charging is not possible. If someone used to have similar problem before, I would really appreciate to hear it from you! I’m becoming really desperate - I don’t know what to do. I just spent my budget on purchasing this car, so I really don’t have any money left for expensive repairs & sneaky mechanics. Please, help me!!

Thanks a lot!