Check the b+ connector under the hood. It can get loose and kill the power to the starter. Also did you measure the battery voltage or monitor the voltage while driving to make sure the alternator is going its job?

New ≠ fixed so follow up as you mentioned on load test the battery. Unfortunately kind of difficult to reproduce if the ambient temperature isn't deep freeze while you had the problem but the load tester does try to approximate the temp current capability

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)