Some things you could try:
Try a "safe boot":
Press the power button and IMMEDIATELY hold down the shift key and keep holding it down.
Can you log in that way?
Try INTERNET recovery:
Press the power button and IMMEDIATELY hold down
Command-OPTION-R
If the iMac connects via wifi, you'll need the wifi password.
The internet utilities take a while to load, be patient.
When loaded, you should see the "utilities" panel.
IF you can get to the utilities, I'd open disk utility.
Then go to the view menu and choose "show all devices".
Then, click on the internal drive (list on the left) and try the "First Aid" function.
Then reboot "normally" and try again.
If you can get this far, but STILL CANNOT proceed past the friend's login screen, then my guess is that -something- is messed up in her account (rather than being "messed up" in the OS itself).
Finding WHAT is messed up can be vexing.
What I would do at that point:
Create a NEW user account with administrative privileges.
This is not difficult to do, but requires "a trick" on a Mac on which you can't get logged in.
You would need to do this:
- get connected via target disk mode (or boot from an external drive)
- locate the INVISIBLE file named "applesetupdone" and DELETE it.
You might be able to do this:
- boot to internet recovery, get to the utilities
- open terminal
- enter "rm /var/db/.applesetupdone"
- quit terminal and reboot
(NO PROMISES on the above terminal command, I've never tried it)
I HAVE deleted the applesetupdone file manually.
WHY YOU NEED TO DO THIS:
When you delete the ".applesetupdone" file, you are tricking the OS into thinking it's "brand new out-of-the-box", and it will present the original setup routine the next time you boot ("choose your language", etc.).
NOW you can create a NEW account with administrative privileges which you should be able to get logged into, even though the friend can't log into HER account (because there's something wrong with it).
This makes it possible to get the Mac running again on its own.
From there you will have to ascertain what's wrong with the friend's account.
If you can't find the problem, there is an alternate course of action:
Create a NEW account for your friend, and carefully "move stuff over" a little at a time to see if that can be done without rendering the new account unusable, as well.
