1990 Toyota Corolla loss of battery power

I just replaced the battery, drove car for the day, parked for the night and the battery was dead the next moring. Recharged the battery and checked the alternater which is perfroming correctly. However again used the vehicle for day and the next moring the batttery was dead. Each day when I start the car cold the battery and brake dash lights appear, go off when brake pedals is depressed only after the car has been engaged and moved. Once car engine is warm, the lights go off and remain off even after restarting. I have no blown fuses. In addtion the over head dome light only works in the "ON" switch position, no light when in the "Door" switch position either when engine is on or off.
Where do I go to resolve the dispearing power from the battery? I would like to have some dependablity from the car as know I am removing the battery cable when I park the car.