Why doesn chmod work?
The most common case is that your /etc/passwd or /etc/group files are not properly set up. If ls -l shows a group of mkpasswd or mkgroup, you need to run one or both of those commands. If you’re using FAT32 instead of NTFS, chmod will fail since FAT32 does not provide any security. You might consider converting the drive to NTFS with CONVERT.EXE. For other cases, understand that Cygwin attempts to show UNIX permissions based on the security features of Windows, so the Windows ACLs are likely the source of your problem. See the Cygwin User’s Guide at http://cygwin.com/cygwin-ug-net/ntsec.html for more information on how Cygwin maps Windows permissions.