Have you tried:
dpkg --configure -a
or
apt-get -f install
?
You will need sudo if using Ubuntu or su if using another Debian distro. Try
the first one first as it relates more to your error message.

No results. Just those funny error messages. I copied everything from the
Terminal now.
What can be done ? In that time I would have done a new Ubuntu clean install
with deleting all the system folders and files except for what I have and
install without formatting.
What other alternatives are there except for reinstalling the system (done
really in 25 minutes) for the sake of one broken package that should not have
been installed after all and which interferes with the package manager ?
After a fresh install, there is 30-60 minutes of fun installing other
software, mainly from the repos.

If dpkg cannot be fixed using dpkg --configure -a then you would be as
well doing a clean install - as has been mentioned many times, any OS
upgrade is iffy at best and can be a pain in the neck !!

As you say, the time to do a clean install isn't that long compared to
the time already taken trying to fix things - at least you won't spend
a whole day trying to catch up like you would in Windows

I would try to remove all of the cached packages because rather than
download it defaults to using the cache.
sudo apt-get clean

then try to completely remove and re-install. It is worth a try. Whether it
is a time saver over a fresh installation is a separate question. You may
re-install and then have it re-occur.

I would try to remove all of the cached packages because rather than
download it defaults to using the cache.