How is the account not logged

Power down.

Safe Boot, (holding Shift key down at startup), does the problem occur in Safe Mode?

See if you can create a new administrator account by restarting the Setup Assistant:

1. Boot into Single User Mode: Start/restart your Mac. As soon as you hear the startup tone, press and hold ⌘ + S until you see a black screen with white lettering. (If you end up back on the login screen after a flash of the black screen with white lettering, enter your password and it will return to the black screen.)
2. Check and repair the drive by typing /sbin/fsck -fy then ↩ enter - as directed by the on-screen text.
3. Mount the drive as read-write by typing /sbin/mount -uw / then ↩ enter.
4. Remove the Apple Setup Done file by typing rm /var/db/.AppleSetupDone then ↩ enter.
5. Reboot by typing reboot then ↩ enter.
6. Complete the setup process, creating a new admin account.

Be very careful to notice the spaces in those Terminal Commands.

Once you've done that the computer reboots and it's like the first time you used the machine, except all your data will stile there. Your old accounts are all safe. From there you just change all other account passwords in the account preferences!!

Hello, it's not quite clear what help you need or where?