a member called Dr Bert had the exact same issue on his W210 and the dealers said it was a dead ECU because their diagnostic equipment showed communication error. His car's electric fans were also blowing with Key on.

His remedy was a new K40 relay which powered up the ECU and started the car perfectly on first crank.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)