THE CAR WILL START AND IDLE, THE MINUTE I TURN ON THE HEAT AND THE LIGHTS AND RADIO IT WILL RUN AND IDLE FOR A FEW AND THEN SHUT OFF ON ME AND THEN THE BATTERY IS DEAD AND I CAN'T START IT UP AGAIN

I would have a load test performed on the charging system. It could be that the voltage regulator is not working properly or the alternator even if new may not be performing correctly. When a car is running the battery is not doing very much besides helping to support even voltage for the vehical systems, but if the charging system is not performing well many thigs will go wrong.

Your problem could just be bad connection to your terminals , i have a had that a few times , that also sounds just like a alternator problem tho , wierd if you already had it tested tho , maybe it could be you have the wrong alternator if your not producing enough amps for your accesories you will run out of power and the car will die