I am wondering if you have a ground issue? Have you removed the ground cable from the battery to the chassis and cleaned the contact? How does your positive battery cable look? They tend to swell with corrosion over time, its also possible to have broken strands of copper near the battery clamp. Did you take the battery in for a charge and testing after you replaced the alternator? I drove my 300d for over a month with the alternator not charging the battery....it seems strange that you can't go a mile before its dead...its also possible the starter could be causing the drain...

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