The worksheet function If() isn't available to Application.Worksheetfunction; I'm fairly certain that means it isn't available to the application object either. Try this instead.
    If cboPart.Value = "Other Customer" Then
        Cells(7, 3).Value = Cells(6, 3).Value
    Else
        Cells(7, 3).Value = Application.VLookup(Cells(3, 3).Value, Sheets("FS").Range("A1:AE100"), 2, 0)
    End If