Ok, so I put the new voltage regulator on and still the same problems persist. Maybe someone can help me out.

Here's a list of what I know.
1) The battery light is on with the key out of the ignition as long as *a* battery is connected. The car battery, jump pack, doesn't matter
2) It wouldn't start without the jump pack, but the battery checks out with my drop tester when fully charged. It cranks slow
3) The battery light turns off once the car is running
4) The alternator charged at roughly 13v when I started it
5) I checked the pulleys and accessories and everything spins freely