Originally Posted by jfoj

Not sure how I would address this problem.

I might back probe the fuel pump power and run the wires into the cabin so I can confirm 100% that there is no power to the pump when there is a no start. You could use an LED or test light.

Have not seen EWS problems with the E70, but we have seen problems with EWS/Keys on the E46/E38/E39 that would crank but not start. Usually another key would be the solution.

Do you put the key in the dash or do you keep the key in your pocket?

Have you tried another key to see if you have the same problem with a different key?

As mentioned, could be a bad connection/ground somewhere that does not like the cold temps.