The barrel is just a key-operated lock mechanism that works two switches - one switch - the first position - is used to energise all the circuits via relays when the ignition is tuned on - that seems to be operating from what you say.
The second switch - for starting the engine - operates the starter solenoid to energise the starter motor - that too is operating.
When the engine starts - and for some reason - the relay that allows the heater fan to run drops out.
I would suspect a defective relay - I just guess - I am not a motor engineer.
Good Luck...
January 2017
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