And definitely there is a measured proper input voltage at the board from the AC cord?
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Since it runs on LP, but throws A4 error, it may *not* be the board.
I'd double check that input voltage right on the board/transformer circuit.
Whatever senses that input voltage is the cause (don't know if the AC input voltage is sensed right on the board).
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Fully possible error cycle is:
SET auto mode
Turn on fridge
Fridge selects AC as priority input
AC input measures too low (A4 error)
Fridge selects LP
Fridge lights LP successfully
Fridge checks to see if AC is present
AC IS present
Fridge selects AC
AC voltage too low
Fridge selects second priority (LP)
Fridge lights LP
Checks for AC
AC present switch to AC
REPEAT - infinite loop