Your alternator is dead. Your voltage regulator can regulate voltage when it is being created, but if it is not being created, there is nothing to regulate.

Charge battery, start car, you should be at 14.4-14.7 volts while charging.

12 volts running means no VR or alternator charge current going to battery.

No matter how responsible he may seem, never give your gun to a monkey!
1970 Coronet Vert
1972 Charger
1974 Satellite Sebring Plus Sundance
2001 Ram 4x4
2002 Intrepid
2006 300C