Very possibly your battery. Do you know how old it is? What is the voltage when not running? Your battery may very well be on its way out and the alternator is working hard to keep it charged. Your alternator isn't eliminated from suspicion at all as it too can be on its way out, but what you describe seems like the electrical gremlins that seem to pop up when a battery and/or alternator are on their way out.

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'01 740i Sport MKIV, Quad Brake Lights, Bi-Xenon retrofit, HID Fogs Dinan 7 Struts, Springs, camber plates, Intake, MAF, CAI, Throttle Body, NBT Retrofit, Strong Strut


'99 318ti Titanium Silver; '97 318ti Boston Green; '13 X5 3.5i Saphire Black Metallic
'84 633csi Black (sold); '88 325iC Black (sold); '97 740iL Black(sold); '01 740iS Black (sold);'97 318ti White (sold); '08 X5 4.8i Titanium Silver (sold); '96 318ti Alaska Blue (sold)