Hi there,
From the symptoms you give, it is likely that you just have a glazed belt. This is a hard problem to believe, but it has happened to me a couple times. What happens is that right after starting, the load on the alternator is high, and the belt slips until either the load decreases or the belt gains enough friction to spin the alternator. Try replacing the belt. Also, check to make sure the drive pulley on the alternator is in good shape.
Let us know the outcome!

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Richard Wooldridge
'01 ML320
'82 300D 4.3L V6/T700R4 conversion
'82 380SL, '86 560SL engine/trans. installed
'79 450SL, digital servo update
'75 280C