Car wont start when engine shuts off radio keeps blowing, when i turn on the A/C the battery light goes out. Tried to jump start it wouldn't jump start right away.

USUALLY WHEN THE BATTERY LIGHT COMES ON THE ALTERNATOR IS NOT WORKING. nothing will work right,because the battery is drained.have charging system tested at parts house,it's free,ALSO, the battery must have a full charge on it before testing.may need to take the battery out and have it charged,and will have 12.6 volts on a fully charged battery.