My Sears Kenmore HE3 washer has a high pitch ringing sound that is coming from the mother board on the front of the washer. It makes this sound even when not running.
Any ideas?

How old is it? You might need to contact customer care about this issue. If anything like a mother board on computers if you have a humming sound or even a ringing sound there is potential that it could cause a fire or even further damage. I am no expert but it's just a thought.