We have been locked out of our iMac running on El Capitan. Basically all known user accounts have disappeared. Only "other" remains which seems to the "system administrator" or "root" and when trying to login with this one, it hangs (endless turning white circle). Have been on forums and tried many of the First Aid (and second aid) tips and tricks, including
fsck (where I found out initially "MacHD had been modified", and eventually got to "MacHD seems to be working fine").
Someone suggested the problem may be in Launch Services area and to access the Mac through FireWire and Target Disk Mode, but I don't have the possibility for such connection, plus without step-by-step I am not tech savvy enough to dare the programming challenge it seemed to require.
Any help would be wonderful. I would bring it in, but as always when things fail, several important docs on the hard drive hadn't been backed up yet, so there we are.