In response to the PasteBin outputs:
You have a lot of additional repositories and PPAs, all of which you need to manually remove before doing the major upgrade.
Without that, who knows what will happen. Nothing good, that's for sure.
Please install ppa-purge package:
sudo apt-get install ppa-purge
And proceed with the removal with maximum caution and remove all of the additional repositories just by moving the files elsewhere from /etc/apt/sources.list.d/.
An example follows:
sudo ppa-purge ppa:whatever/ppa
More importantly, you need to downgrade all packages to trusty or rosa if it is specific package used by Mint.
The Linux Mint 17.x is based on Ubuntu 14.04 Trusty, so for example:
sudo apt-get install adwaita-icon-theme/trusty
or
sudo apt-get install adwaita-icon-theme/trusty-updates
or
sudo apt-get install adwaita-icon-theme/rosa
The commands are ordered by success rate from the highest, but I recommend to try it in this order:
rosa
trusty-updates
trusty
It's a lot of work, I realize that, but I myself have done it and successfully.
Reasoning: Most probably one of the PPA or additional repository upgraded adwaita-icon-theme and other packages. The underlying reason being that you would de facto have newer version already installed of some packages which causes dependency issues. Hope my answer helps a little
EDIT1:
In response to the comment of non-existend package:
there is no such package named adwaita-icon-theme
There is adwaita-icon-theme and the others in Ubuntu Xenial which is the base for Linux Mint 18.x.
In response to the comment of restoring PPAs:
if I purge all PPA and fail how can I restore them?
Simply edit the PPA source files located in:
/etc/apt/sources.list.d/
And remove the # beginning character.
You can try installing the apt-show-versions:
sudo apt-get install apt-show-versions
The usage is simple, call the program and grep results you are interested in.
It could, with some effort, resolve your problem with identifying the packages to downgrade. As I said, you need to downgrade all packages prior to proceeding with major system upgrade, so if you have already removed the PPAs and other repositories, now go ahead and downgrade what you can to trusty as mentioned above.
If you have multiple computers, then it's very simple to set-up SSH. Why SSH? Well, no upgrade with a lot of system adjustments goes smoothly and rather than being stuck at the console, I mean VT1, and typing all from your head, when things go south (and they most probably will), it's much more convenient to sit at another computer and communicate with the world for instance about what the hell happened.
I personally would go ahead with the upgrade right now, ignoring the problem, and I would solve it via SSH from another machine later when it happens. I have managed to convert KDE to Cinnamon editions and upgrade them later, it can't be harder than that. I think it will be a piece of cake, at best you'll learn a few usable commands, and at worst you restore your drive from backup.
BACKUP:
One way to make a totally perfect backup of your drive is:
Boot from a live USB with Linux Mint.
Install pv utility:
sudo apt-get install pv
If you have multiple drives, make sure you find out witch one is the one with your Linux Mint 17:
sudo fdisk -l
Suppose you have one system drive and one external HDD for the backup /dev/sda, then it would be as simple as clicking on the external HDD in Nemo, that will mount the drive and then:
sudo -i
pv < /dev/sda > /media/username/drivename/backup-sda-pv
