No water to the ice maker

The "through the door" water is working fine, but I am not getting water to the ice make. I checked the fill tube and it is not blocked. I put the icemaker through it’s full cycle (heat, dump ice, refill) and at the refill point the selonoid/valve at the bottom rear of the refrigerator hums (or buzzes) for a few seconds but no water. I am guessing that it is the valve, but I would like a second opinion.