"if I wipe the hard drive, install OS X again it boots with no problems."
OK, here's what I'd do in your situation:
1. Get the Macbook booted from an external drive. You want to be able to "boot it to the finder".
2. Once booted, use either CarbonCopyCloner or SuperDuper to clone the internal drive to ANOTHER external drive of some sort. Or... if you can get the internal drive mounted in the finder, just do a finder copy of the files you want to save (such as your mother's home folder) to another location. The purpose of doing this is to preserve whatever user data she has on the MacBook.
DO NOT try to use Time Machine for this. You want the backed-up files to be "finder visible" and "finder copy-able".
3. Once you have salvaged her data, NOW it's time to do a clean installation of the OS onto the MacBook and get it "bootable again".
4. Can you get this far? If so, create a new account for her, and get her up and running in her new account.
5. Now it's time to get her old data back. Be aware that if you try to copy from the backup source (without doing the following), you may encounter permissions problems.
SO.... you have to:
a. connect the backup drive so that the icon for the drive is visible on the desktop
b. open the GET INFO window, and at the bottom "unlock" it
c. put a checkmark into the box "ignore ownership on this volume"
d. close the GET INFO box.
You can now copy files from the backup to the new account and not be bothered by permissions issues.
Can you get this far?
