First thing to come to mind would be the ignition switch. They are known to give trouble so replacing that wouldn't be money wasted if it isn't at least part of the problem. The battery and charging system need to be in good shape on these vehicles as well.

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1988 325is (purchased new) sold
2004 X5 3.0 2005 X3 2.5
2008 X5 3.0 (new to me)