Cadillac Fleetwood Brougham Engine Not Running

I Just Got This Car Off My Brother N Laws Uncle And They Had It Runing, At The Time They Installed A New Distributor And Its In Time But...

When You Cut The Heater On A Belt Start Squilling And When You Cut The Car Off Then Try To Start It The Battery Is Dead What Could Be Wrong

To Start With. Last Time I Drove The Car At The Start Up The Engine Coughed And Choked For A Good While Before Finally Idling Normally....