Not necessarily. Er-01 is as you say, quite literally a communication error between the ECU and the dash - the dash is not receiving a signal from the ECU. This is why you couldn't enter the diagnostic mode.

You have done the right thing in checking the connector at the dash, but you need to trace and check every last piece of wiring back to the ECU and the ECU multiplug itself. Make sure the terminals and connections are good and that there are no bare wires or damaged insulation. It could be just a case of drying everything out if you've been riding through a lot of deep water?

Because you did/could get it to run, I would suggest the ECU is OK. It could also potentially be an immobiliser fault? Have you got another key you could try?

BTW - Did it actually overheat when the temperature warning LED lit up? Or was that a false alarm?

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