You might have a poor connection at the safety disconnect (BST I think it's called) on the positive terminal or maybe the firewall terminal. Do some more testing with your multimeter and try to do some with a load on or maybe a helper trying to crank. Another good example of why everybody should really have 2 working keys!

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