Check the voltage at the starter when spinning. The starter motor winding itself provides the ground for the solenoid pull-in winding to engage the starter so for the original and the replacement starter to have the exact same problem is highly unlikely. Better chance there is only enough current available to spin the starter motor without pulling in the drive. Maybe a ground issue. Try using jumper cable.

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