Are you sure the trunk light is off?
Something must be drawing power with the ignition switch off. If you know how to use a current meter* , you can probably figure out where that current is going.
Set the meter to read current in the order of 200mA. With the ignition key off and the doors closed, pull out each fuse and put the meter across what that fuse plugs into. You shouldn’t see any appreciable current flowing.
If one does flow a lot more than any other, that’s likely the curprid. Whatever that fuse protects is drawing more current than it should. See what happens after four days with that fuse out. If you can start the car, there’s something that needs to be checked.
(*a multimeter like this has that function: http://www.harborfreight.com/7-function-multimeter-98025.html)