Your model is empty because you didn't pass anything to the View. Note there is nothing inside the parenthesis:
So, since you didn't pass anything to the view, your references to "model" in the Razor code will all be null:
@Html.DropDownListFor(model => model.PartTypeId, (IEnumerable<SelectListItem>)ViewBag._PartTypes)
Don't use the ViewBag if you're using MVC. It's just going to confuse you.
The purpose of the Model is to pass any data to the view that renders the HTML any data it needs to build the HTML, including the contents of DropDownList's.