Backup from within recovery mode

Try copying individual file via Terminal in Recovery

Copying Files to External Hard Drive via Terminal When booted to Recovery?

There are several ways to back up a Mac that is unable to fully boot. You need an external hard drive to hold the backup data.

1. Boot from your recovery partition (10.7 or later), a local Time Machine backup volume (10.7.2 or later), or your installation disc (10.6.8 or earlier.) Launch Disk Utility and follow the instructions in the support article linked below, under “Instructions for backing up to an external hard disk via Disk Utility.”

How to back up and restore your files

2. If you have a working Mac, and both it and the non-working Mac have FireWire ports, boot the non-working Mac in target disk mode by holding down the key combination command-T at the startup chime. Connect the two Macs with a FireWire cable. The internal drive of the machine running in target mode will mount as an external drive on the other machine. Copy the data to another drive.

How to use and troubleshoot FireWire target disk mode

3. If the internal drive of the non-working Mac is user-replaceable, remove it and mount it in an external enclosure or drive dock. Use another Mac to copy the data.

Hi, I'm stuck at step 9 to backup by writing a DMG to my external harddrive. I don't see my external harddrive when I want to save the DMG backup file. Can you please help me with this? I'm desperate to make this backup! Big thanx in advance!

<E-mail Edited by Host>

I'm having the same issue, but when I try to back it up through disk utility or repair it, it fails every time.