Bad alternator or voltage regulator or very bad(broken) connection somewhere. Make sure the alternator is turning. Does the car have a voltage gauge in the dash? Check it, it should read about 14 volts. If not, is the idiot light for the charging system on?
It sounds from your description as though the vehicle is not charging the battery, rather than having a drain when its off.
If everything works okay, lights, heater blower etc while the vehicle is running, and the battery is new, I would start by looking for a bad connection to the battery.