When you first start a washing machine, the very first thing it does is fill with water.
Can you check to see if the noise it's making occurs while it's filling with water or only once it starts to agitate. If it makes that noise while it's filling, switch the temperature setting from warm to both hot and cold and see if the noise goes away on one setting.
If it makes that noise while filling with water, it's a minor problem. It's probably simply a loose washer in the water supply valves you hooked the washer up to. In that case, the washing machine would have worked fine in your neighbor's house, but it's the rubber washer in your water supply valves that's loose, and that's why it's making a racket in only your house. Alternatively, it could be a leaking diaphragm in the water mixing valve inside the washer.
If it doesn't start to make that noise until it begins to agitate, then it's a mechanical problem and could be darn near anything, depending on the make and model of washing machine.