Not sure of the year, make model or engine but you obviously have a vacuum leak. It may or may not have anything to do with the booster. When you step on the brake pedal it pulls engine vacuum for assist. If you already have a vacuum leak this will kill the motor. It will run on its own while cold because the choke plate is closed increasing engine vacuum. Did you plug the brake vacuum line off at the intake? How about the PCV line? Could have a bad intake gasket as well. Check all under hood vacuum lines for splits and cracks. Get a helper to keep the engine running and listen under the hood.
~Michael
