White smoke indicates unburnt diesel. Does it smell of diesel from exhaust? sounds as if diesel pump or injector fault. When you say it has drained the battery do you mean it wont start or lights etc dont work. If lights etc ok then likely to be sensor saying no to engine going.
2002 Toyota Avensis: You could have a bad fuse in one area and, you may have bulb connector issues in another area. Check your bulb retainers be sure the terminal connectors are free of corrosion. You can clean these connectors with electrical spray and a small, thin wire brush. https://www.youtube.com/watch?v=4IfKCtX0wm4
