Do you have an alarm with battery backup? If you do, the 'start' process is draining the car's battery to the point that it cannot keep enough voltage to the alarm siren. The siren thinks the battery has been disconnected, and "goes off", using its own battery for power. When you stop cranking, external voltage is restored to the alarm siren, and it turns off.
The symptoms are coincidental. Did you have the stereo going while you were doing all this work on the car?
Try jump starting the car. But you may well need a new battery.