impossible to log in after changing password on iMac 2009

I decided to change the password I used since buying the iMac (you should not do that on a Friday 13th). The iMac went to sleep. When I tried to wake it up, impossible to log in with the new password or with the old one. In the top right corner, there was a message only partly visible, something about the need to finish the process by entering something more. But no way to read the full message or to log in therefore I restarded the iMac and got the same result. Since then, several restart and the same.

I called Apple support and learnt that my iMac was "vintage", i.e. 2009 and not supported any more. The guy was nice but did not give me even the beginning of a hint : known bug ? mistake in typing the new password ? (twice the same typing mistake ?).

Looking through the communities, it seems there are a few issues with passwords, but nothing exactly like that. Our computer guy at the office told me about some issue happening sometimes with capital letters on iMacs and recent OS.

I tried to reinstall OSX, not to loose my data. Sucessfull but then same password issue. No success with hard disk utility tools. I have a Time Machine backup but not updated in the past few days and hoped to avoid using it as I had just had the installation of a VPN.