When you typed [tt]chmod -R 777[/tt], it was in the Cygwin console on the Windows box, right?
You need to find the real folders that the folders in your Cygwin console map to.
I think, in Cygwin, your home is c:\cygwin\home\<name> and your root is c:\cygwin. Everything on drive C, relative to the Cygwin console is below /cygdrive/c. That might not be exactly right, but it's close. Change those files' permissions using Explorer (not IE, the regular file explorer).
If that fails (this has happened to me), you will have to use the venerable Windows Command Prompt (Start -> Accessories -> Command Prompt) with the attrib command. Find the offending files and use the command [tt]attrib -r[/tt], then [tt]attrib -s[/tt] on each of them. It's a tedious process and, as far as I know, Windows/DOS batch file scripting is incapable of speeding it up.
When you untar the file, does it create some of the files, just not all of them? It occurs to me that it might create a directory you don't have write or execute(search) permissions to, then try to extract files from the same tar file to the directory it just created. It could create the directory, but not the files because of the directories permissions. This means you would have to untar, then [tt]chmod -R[/tt] the new directory, then untar again.
These are just some ideas. I don't think that the problem lies with the tar program you use, but in interpretation of the file and directory permissions. Effectively, you're root in your Cygwin console, so you can tar files that you can't read. But you're not root on your Linux box, so you can't untar them.
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-- Ghodmode