The hard drive on my Macbook is corrupted and so I am trying back up files from the hard drive on my Macbook to a target disc so that I can wipe the hard drive on my Macbook and re-install the system software. I am only able to access the Macbook via disc utilities using the start up system DVD. Is there a way of accessing the files while I'm in disc utilities so that I can transfer to the target disc?
Some MacBooks have Firewire, while others do not. See this tip:
https://discussions.apple.com/docs/DOC-2502
If both of yours have Firewire, you can use the Target Disk mode described at the end of the tip. Otherwise, you'll need to pull the hard drive out of the machine that it is in, and put it in a 2.5" hard drive case that supports the ports that are on the other machine.
Note, if you can't read the data on the other machine, using a data recovery tool to a hard drive at least as large with no data on it is recommended. This tip explains how to do data recovery:
how can I transfer files from my macbook pro hard drive to another target drive
