Using NTFS "traverse" permissions, but user still denied access to network share (SBS 2003)

You want Traverse Folder and List Folder like you've listed and you want to set the drop down at the top to This folder only. Then you need to set whatever other permissions you want that user to have on the explicit subfolder that they should have access to.

If you can't get into the root folder with what you've posted, it's likely because of the folder's share permissions and not the NTFS permissions - double check those.

All users have the Bypass Traverse Checking user right by default, so my suggestion would be to not assign the permissions for the user the way you have but instead to assign the permissions for the user only on the file you need them to access and then give them a shortcut to that file. That will allow them to access the file without having to directly navigate through the shared folder to find the file.

http://technet.microsoft.com/en-us/library/cc739389(v=ws.10).aspx

If you need them to directly traverse/browse the shared folder structure then you'll have to do it the way MDMarra suggested in his answer.