On Mon, Jun 5, 2023 at 10:15 AM François Patte <francois.patte@mi.parisdescartes.fr> wrote:
Bonjour,

Today I tried to upgrade from fc34 to fc36.

Downloading the package was okay.

What package? 

From: https://docs.fedoraproject.org/en-US/quick-docs/dnf-system-upgrade/#sect-how-many-releases-can-i-upgrade-across-at-once
"... it is highly recommended to perform the upgrade before your release reaches End of Life (EOL).   "

Around release time for a new version there are updates to prepare for the next release.  If fc34 did not get all updates, those could
be missing.
 
Problems occur when I agreed to
system-upgrade-reboot:
1- No display... I could only dee the led showing HDD accesses
2- After sometimes (when no more accesses were showed, I press enter key
on the keyboard and the system rebooted on fc34 kernel and still no
display...
3- I pressed the "y" key on the the keyboard (in case the system upgrade
was asking some question...) and the display came (hurray!) : I could
see the login screen of the fc36 version. I could login but all my
previous display settings were gone....
4- I checked the kernel with command uname -r and it is stille the fc34
kernel which running... No f36 packages have been installed in /boot....
5- many packages from fc34 remain installed and only some fc36 packages
have been installed.

What can I do to have a coherent fc36 install now?

You will probably have to do a fresh install. 

--
George N. White III