Problem with permissions
First, as an FYI, you only need to boot into the recovery partition to repair permissions when you are trying to repair permissions on your computer's boot drive. To do it for any other drive, simple select it in Disk Utility and click the Repair Disk Permissions button. This may solve your problem, so try that first.

After that, the simplest solution is to turn on "Ignore Ownership" on the drive. Navigate to the drive in Finder and use Get Info... to see the permissions, as you have been doing. Underneath the permissions, you'll see a box that says "Ignore Ownership on this volume." Check that box. This will ignore all permissions on the volume and allow any user or program to do anything on the drive. Follow this link for more information on the benefits and perils of doing this: https://larryjordan.com/articles/mac-os-set-hard-drive-permissions/

Alternatively:

You can reset the permissions using the Terminal App. Open the app in Applications > Utilities > Terminal. 

Navigate to the folder you're having trouble with using the "cd" command, then use the command

sudo chmod -R 644 .


This will change the directory and every file within that directory to the default OS X permissions. For more information on how to use Terminal and chmod, take a look at this tutorial:

http://computers.tutsplus.com/tutorials/navigating-the-terminal-a-gentle-introduction--mac-3855