Dead HD, using Linux Live CD to recover data

My hard drive, after a few death throes, has stopped booting altogether. However, I tried booting to single-user mode and I could view all the files in my home folder. Couldn't copy them out to an external HD though, since I couldn't mount it. So, booted from an Ubuntu Live CD, got the internal HD mounted to /mnt/mac, and mounted the external HD to /media/disk.

But, when I try *sudo cp /mnt/mac/Users/me /media/disk* it tells me
*"omitting directory 'mnt/mac/Users/me'"*. In fact I can't view any deeper than my home folder in Linux. Any ideas what's going on, and how to rescue my files?