I am running into a similar issue. I have a disk from a laptop and want to clean it up. I connected it to my desktop and could not delete cygwin and its subfolders although I am in the admin group on the desktop. Even when running Explorer as Administrator.
Solution: right click on cygwin folder, choose Properties, then Securtiy tab, Advanced Security. On that dialog, choose the "ownership" tab. Edit ownership, and make it yourself. The problem was that the folder was owned by a user on the laptop, who no longer exists.
Make sure to check "replace ownership on subfolders and objects". Hit apply and let it run through the +100k files that cygwin has.
Is this enough? Unfortunately, frustatingly no! Then you have to go into properties, security, and edit,and allow delete on the folders. I just set Everyone to full control because I'm just trying to delete the freaking folder, for goodness sake. Also make sure that the change is propagated to all child folders and files.
Now, at last, I have removed cygwin files and folders from the drive. Next I will archive off some other things before deciding what to do with this old, but still usable drive.