Glad it worked out for you, but you replaced the alternator without verifying that the old one was bad. I just finished troubleshooting the system on my son's car and determined that he had simply run the battery down accidentally (he left the stereo on). But, the car is 9 year old and the battery 3 years plus, so I followed the following steps...
Visual inspection of the battery wiring (saw nothing obvious)
Cleaned the batt terminals (a little dirty)
Checked fluid level in all the battery cells - all good
Charged the battery (Multimeter read 13.0 volts when my smart charger said it was 'FULL')
Let it sit overnight to let the surface charge dissipate (got 12.62 volts. Perfect)
Load tested the battery (gauge fell right on the CCA rating of the battery)
Tested the alternator (14.42 volts. Perfect)
Load tested the alternator (ranged from 14.2 to 14.5 volts with headlights and heater blower on. Perfect)
The whole process took 12 hours or so (mostly letting the battery sit overnight), but everything got a clean bill of health and I can confidently give the car back to him and just tell him 'don't do that again' :joyous:
Not picking on you at all, but $50.00 worth of test equipment (digital multimeter and battery load tester) can save you many hundreds over a few years.
My .02