How to access restricted files from hard drive that won't boot

My Macbook Pro (10.9.3) wouldn't boot up. I'd get the gray spinning progress indicator along with a gray progress bar which would get about 10% through and then restart.

I booted into recovery mode and run Disk Utility to repair the disk and got a message saying can't repair, back up your files.

So I took the HDD out and mounted it as an external drive on my Mac Mini (10.9.3). I got a message saying it's read only and I should back up my files. I can browse to my users directory and see all the base folders (Movies, Music, Docs, etc), but there's a red no entry icon on all the folders and accessing them through Finder shows they are empty.

I browsed the files through Terminal as super user and can see the files. I can also copy the files through Terminal. However, after copying a test directory some of the files are read only and others are still no access.

So the question is, how do I back up these files and maintain permissions?

Thanks!

PSA: Go do a backup. Don't feel my pain.