You have one, fully functioning key right? I agree with you, I don't see how it can be a problem with the EWS if the orig key starts the car and the new key doesn't.
Getting keys from a dealer that don't work (start car) is relatively rare, though I think it does happen.
You can't simply return the key as non-working for a refund? If you can, I would return the key and IMMEDIATELY place a new key order with
https://www.thebmwminipartstore.com/.. I would try to avoid having the same key sent back to you (all come from BMW New Jersey)
I don't like the idea of digging out your EWS, struggling with INPA (although you should get it to work), looking at fuse boxes, chasing Zebras, etc. just because you bought a key that doesn't work in this situation. Return it..speak to the manager.