1998 Dodge Caravan alternator

When I go to start my car it will not turn over, It makes a buzz sound, Then 3-4times turning it over it will start, Now that it is below freezing it will not start at all, I tried to jump it and it took awhile to start it, I let the car run for5-minutes and it will not start, just a buzzing sound, Is the voltage in the alternator just low enough where it will not turn over the engine, This is the orininal alternator, Or is it something electrical.