1988 Lincoln Town Car Dead Battery

My car wouldn't start but up till that day had been running great. Got the battery checked and was told it was Stone Dead. 6 years old and we have had very cold weather this year. Replaced with a new battery from Advance and it fired right up. Drove it home and 36 hours later when I went to go someplace it was again Stone Cold dead. I jumped it off and parked inside my garage so I could put the trickle charger on the battery. I did disconnect the hot cable as I got a feeling something in the car is pulling it down. Can't tell about the Alt, with the red lights but it goes out when it is running. Could this model have something besides the clock that is drawing power from the battery? Radio is off and no lights were on. It does seem to have the original Alt on the car and I am suspecting it might be the problem but why would it run down just sitting there for 36 hours not running? Big George