I think you can rule out the ignition switch because if the switch was bad the car would still crank and not start... I believe you should begin with the alternator, because these vehicles are always drawing power even when their not moving; therefore I think your battery is being drained and not being recharged by the alternator. Can you get the car to a shop or the alternator to a shop to get it tested. If the starter was bad your vehicle would still try to start... Just my two and a half cents worth...
V/R Zachary Pullins Sr.
National Capital Chapter BMWCCA
NCC Member Recognition Chairman
NCC High Performance Driving School Registrar
NCC Auto-X BOD Liaison
DIY Senior Committee Coordinator
2006 E90 325Xi & 2000 E46 3XXi
" Vision without resources is just hallucination"