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Yes you need a new pump for sure. You need to pull the unit out an then tip it over to get at the motor. Then it is a basic replacement, here is a image to show you.
So you have just a new drain pump?
I am not sure what would be making the buzzing sound on it, that is not right unless something is rubbing or vibrating. Does it work though?
You may have received a defective motor, I am not sure not else would cause that.