If you need to press the down arrow key and your list items have the "Keys" method, you can just code the following in vbscript inside a loop:
listObj.Keys("[Down]")
(You can search the TestComplete help file for "Keys Method" for more information.)
Then, you can compare the list item's appropriate property value to the given value. Note that which properties are availabe depends on how TestComplete sees the object (which may be affected by which Open Application properties are set and the priority of them within TC's Project/Properties configuration).
One example I have is how I accessed a FarPoint spread control's cell values in a list and compared them with a value in a search variable, which is:
if obj.cells.get_item(rowIdx,colIdx).TextOleValue = searchValue then...
Hope this helps...