I cannot unlock the lock on administrator account

You might try resetting the admin password as described here:

Changing or resetting an account password

Reboot and hold the option key when you hear the chime, when the boot manager appears select the DVD.

I assume that you can read the DVD when you are booted into OSX?

Boot up with command - S as you did before, once at the prompt enter these lines, one at a time (hit return after each line)

• mount -uw /
• rm /var/db/.AppleSetupDone
• shutdown -h now

Then restart, you will be in a new administrator account which will allow you to make the changes you need to the old account.

If you can't do this (because it does work) take your Mac to the Apple Store.

http://osxdaily.com/2011/04/25/change-admin-password-mac/

mikolajjj wrote:

Yep, I tried that too 😟 As I wrote, on the new administrator account I also cannot unlock the lock.

Why do you think should I take my Mac to Apple Store? Does it seems to you as a hardware problem? Or do they have some tricky ways to undo everything?

Acctually I found kind of a tricky way on a web, but I follow its steps as a monkey so again with no succes. These are unix commands to abstract for me. Do you understand the logic? Do you think it might help with my problem?

Or maybe I can login as root (somehow) and that could let me change password of my account?

I understand that all the usual methods have failed for you, even though they work everytime for me, that being said there are only 2 reasons for this, there is something else wrong with your Mac or you are not able to type the commands as needed (I am not choosing which, just stating the obvious).

Either way you now need hands on help, I do not advise tampering with the machine as the Root User, mistakes in Root mode will certainly make things worse.

My bad, reading too quickly and didn't see you had already posted that.