Hopefully I've attached the right files you need.

At the moment, I can't run updates because the same error pops up. At 
boot I get a red 'STOP' icon in the top right corner of the menu bar and 
if I try to update I get a message telling me the "Package system is 
broken". Following the instruction to run "apt-get install -f" results 
in a list of 'no longer needed' files then:
"The following additional packages will be installed: python3"
"The following packages will be upgraded: python3"
"1 to upgrade, 0 to newly install, 0 to remove and 10 not to upgrade."
"10 not fully installed or removed"
"Need to get 0B/8,696 B of archives"
"After this operation 0B of additional disk space will be needed"

After continuing, this is the dialog:

Do you want to continue? [Y/n] y
Setting up python3.5-minimal (3.5.3-1) ...
Traceback (most recent call last):
   File "/usr/lib/python3.5/py_compile.py", line 6, in <module>
     import importlib._bootstrap_external
   File "/usr/lib/python3.5/importlib/__init__.py", line 57, in <module>
     import types
   File "/usr/lib/python3.5/types.py", line 166, in <module>
     import functools as _functools
   File "/usr/lib/python3.5/functools.py", line 23, in <module>
     from weakref import WeakKeyDictionary
   File "/usr/lib/python3.5/weakref.py", line 12, in <module>
     from _weakref import (
ImportError: cannot import name '_remove_dead_weakref'
dpkg: error processing package python3.5-minimal (--configure):
  subprocess installed post-installation script returned error exit status 1
dpkg: dependency problems prevent configuration of python3-minimal:
  python3-minimal depends on python3.5-minimal (>= 3.5.3-1~); however:
   Package python3.5-minimal is not configured yet.

dpkg: error processing package python3-minimal (--configure):
  dependency problems - leaving unconfigured
No apport report written because the error message indicates it's a 
follow-up error from a previous failure.
                             Errors were encountered while processing:
  python3.5-minimal
  python3-minimal
E: Sub-process /usr/bin/dpkg returned an error code (1)
brian@VideoEd-Linux:~$

I hope this is helpful. I have not tried removing python references from 
/usr/local as Dave Kuhlman tried but unless any other ideas come up, 
I'll try that shortly.

Brian Kelly.

On 19/04/2017 16:37, Brian Murray wrote:
> On Wed, Apr 19, 2017 at 03:09:41PM -0000, Brian Kelly wrote:
>> On 18/04/2017 21:48, Brian Murray wrote:
>>> How did you go about upgrading from 16.10 to 17.04? If you used ubuntu-
>>> release-upgrader please include the logs in /var/log/dist-upgrade/ so I
>>> can better sort out how things went awry.
>>>
>>
>> The upgrade was from the GUI following a regular update. I followed the
>> 'new version is available' route and accepted the defaults at each stage
>> of warnings about removing old packages.
>>
>> There are 5.8Mb of files under /var/log/dist-upgrade on my machine, do
>> you need them all?  I ask because 'broadband' here means 0.1Mb/s so it's
>> a long upload for me!
> 
> The sub-directories should be about previous release upgrades, so those
> won't be necessary. You could confirm you are uploading the right log
> files by looking at the 'main.log' file and checking the date in it in
> addition to looking for the right releases in lines with PreCacheOpen
> and PostInitialUpdate.
> 
> The file 'apt-clone_system_state.tar.gz' may not necessary so you can
> skip that in your initial upload.
> 
> --
> Brian Murray
>