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"BKL_PWM 0.44v"
Too low.
There is PWM signal, but DC value on a DMM should be higher however.
Do few PRAM reset first.
If no result, remove R7704 and run a wire from R7715 to C7704.
Confirm maxim backlight in this case (I hope).
Do again PRAM reset and finally resolder board in original state.
Let us know if then works.
BTW, backlight circuit of 00165 has lot of threads on the forum; just use the search function...