O problema é que o KDE está apenas parcialmente instalado, portanto está em conflito com o GNOME e o gerenciador de pacotes. Primeiro remova o KDE. Então instale o GNOME 3. Por favor, comente se precisar de mais ajuda.
Ontem eu instalei o KDE Plasma no meu Ubuntu 16.04.1 como mencionei nesta pergunta "Falha ao buscar" ao instalar o KDE e tinha um problema de tela preta. Eu poderia fazer o login com o KDE e tinha o ponteiro do mouse, mas não pude fazer nada além de sair. Um dos meus amigos no chat do askubuntu sugeriu que eu instalasse um desktop mais leve, eu peguei o Gnome 3, mas infelizmente não sei por que ele não é instalado. Eu corri sudo apt-get install ubuntu-gnome-desktop e consegui este resultado:
Reading package lists... Done
Building dependency tree
Reading state information... Done
You might want to run 'apt-get -f install' to correct these:
The following packages have unmet dependencies:
kde-telepathy-minimal : Depends: kde-config-telepathy-accounts (>= 15.04.0) but it is not going to be installed
ubuntu-gnome-desktop : Depends: adwaita-icon-theme-full but it is not going to be installed
Depends: brasero but it is not going to be installed
Depends: dconf-editor but it is not going to be installed
Depends: fonts-cantarell but it is not going to be installed
Depends: gdm3 but it is not going to be installed
Depends: gjs but it is not going to be installed
Depends: gnome-backgrounds but it is not going to be installed
Depends: gnome-color-manager but it is not going to be installed
Depends: gnome-contacts but it is not going to be installed
Depends: gnome-control-center but it is not going to be installed
Depends: gnome-documents but it is not going to be installed
Depends: gnome-logs but it is not going to be installed
Depends: gnome-online-accounts but it is not going to be installed
Depends: gnome-session but it is not going to be installed
Depends: gnome-settings-daemon but it is not going to be installed
Depends: gnome-shell but it is not going to be installed
Depends: gnome-shell-extensions but it is not going to be installed
Depends: gnome-sushi but it is not going to be installed
Depends: gnome-themes-standard but it is not going to be installed
Depends: gnome-tweak-tool but it is not going to be installed
Depends: itstool but it is not going to be installed
Depends: libnss-myhostname but it is not going to be installed
Depends: mutter but it is not going to be installed
Depends: ssh-askpass-gnome but it is not going to be installed
Depends: tracker but it is not going to be installed
Depends: ubuntu-gnome-default-settings but it is not going to be installed
Depends: yelp-tools but it is not going to be installed
Depends: zsync but it is not going to be installed
Recommends: a11y-profile-manager
Recommends: deja-dup-backend-cloudfiles but it is not going to be installed
Recommends: deja-dup-backend-s3 but it is not going to be installed
Recommends: empathy but it is not going to be installed
Recommends: evolution but it is not going to be installed
Recommends: gnome-accessibility-profiles but it is not going to be installed
Recommends: gnome-getting-started-docs but it is not going to be installed
Recommends: gnome-music but it is not going to be installed
Recommends: gnome-photos but it is not going to be installed
Recommends: gnome-weather but it is not going to be installed
Recommends: ibus-pinyin
Recommends: mcp-account-manager-goa but it is not going to be installed
Recommends: numix-gtk-theme but it is not going to be installed
Recommends: plymouth-theme-ubuntu-gnome-logo but it is not going to be installed
Recommends: plymouth-theme-ubuntu-gnome-text but it is not going to be installed
Recommends: ppa-purge but it is not going to be installed
Recommends: rhythmbox-plugin-magnatune but it is not going to be installed
Recommends: telepathy-idle but it is not going to be installed
Recommends: ubuntu-gnome-wallpapers but it is not going to be installed
Recommends: xserver-xorg-legacy but it is not going to be installed
E: Unmet dependencies. Try 'apt-get -f install' with no packages (or specify a solution).
O problema é que o KDE está apenas parcialmente instalado, portanto está em conflito com o GNOME e o gerenciador de pacotes. Primeiro remova o KDE. Então instale o GNOME 3. Por favor, comente se precisar de mais ajuda.