16.04 - Authentication error at login after online upgrade to 18.04

I tried an online upgrade from 16.04.2 to 18.04.2 in February 2019, but have never been able to get beyond the initial GUI log-in that comes after grub, due to it always showing Authentication error.

Here's what I've tried so far...

3 posts to Ubuntuforums:

Noticed my GUI login username is showing with an initial capital letter whereas my correct username starts with a lower case. pressed "not shown" and tried entering correct username but had similar authentication error result.

Ctrl+Alt+F3 and try tty3 log-in: successful with lower case username

$ # brought up a small GUI display in top left hand corner of my
$ # screen, but too small to read what it said
$ sudo startex

$ # didn't fix my GUI login
$ sudo chmod 7755 /usr/lib/policykit-1/polkit-agent-helper-1


$ sudo apt install -f
0 to upgrade, 0 to newly install, 0 to remove, 5 not to upgrade

$ sudo apt-get update
fetched 432Kb in 2s

$ sudo apt-get install ubuntu-desktop
already newest version (1.417)


$ sudo apt-get install gnome-core lightdm
unable to locate package gnome-core

I've read Ask Ubuntu answers to these questions:

and all in all I've been struggling for over a month to get my ThinkPad L520's 18.04 to work without any success, so looking now for suggestions that might help me as a slow old codger with somewhat diminished cognitive abilities to get somewhere with this disabling problem.

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Having worked through Simon's suggestions, I still haven't found out exactly what isn't working properly or managed to fix anything, so below, I'm feeding back the results of what I've tried in the hope of getting more suggestions

Try to fix the "5 not to upgrade" with

sudo apt-get dist-upgrade --yes

Some upgrading did take place this time, but as I was working on tty3 I couldn't make a copy of what it did. At this point I went back and tried a GUI log-in again, but no improvement; still got the same brief authentication error message flashing up as before, followed by a blank grey screen that failed to respond to anything other than a restart

Login in the console as you did with ctrl+alt+F3 and check the output
of ps axf

This generated a long output list, which again I was unable to copy, but output was only in the range from 195 to 1621, so no results for 1838 to 2276.

monitor the auth and syslog and return to the login screen
ctrl+alt+F1

sudo tail -f /var/log/syslog /var/log/auth.log

To see this result, I used my live 18.04 -2 DVD disk to load a LIVE session and navigated to /var/log from there.

The auth.log I found covered 2 hours of my trials and errors, so as it's 281kB I thought it best to upload it to my OneDrive cloud folder where there are also some camera pics of my GUI log-in failed attempts.

Analysing this lengthy auth.log file and trying to work out what's going wrong is beyond my ability. Hopefully uploading this auth.log will trigger some further suggestions about what to try, which I should be in a better position to personally deal with by the 2nd week of May.