Car runs with no alternator

Car runs with no alternator but with the alternator hooked up the car starts and then shuts off immediately. Any suggestions new alternator bought from GM so its the right one.

Have you had the alternator tested to verify that it's not defective?

It sounds like you have a short. Are you blowing any fuses? The short could be in the alternator itself or in the wires from the battery to the alternator. Did the car sit for a long where rust could have caused a short?

Not at all. It was always running great but the this problem began happening about 2 days after i put in a new heater core but it ran great for those two days.