Unable to upgrade/install Plesk on Ubuntu/Debian: the following packages have unmet dependencies

Symptoms

Plesk installation or upgrade on Ubuntu/Debian OS fails with the following error:

PLESK_ERROR: Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming.
The following packages have unmet dependencies:
apache2 : Depends: apache2.2-common (= 2.2.22-13+deb7u3) but it is not going to be installed
apache2-mpm-prefork : Depends: apache2.2-common (= 2.2.22-13+deb7u3) but it is not going to be installed
Depends: apache2.2-bin (= 2.2.22-13+deb7u3) but it is not going to be installed
mysql-server : Depends: mysql-server-5.5 but it is not going to be installed
plesk-base : Depends: sw-engine (>= 2.13.8) but it is not going to be installed
plesk-core : Depends: libcurl3 (>= 7.16.2) but it is not going to be installed
awstats : Depends: perl:any
libapache2-mod-bw : Depends: apache2-api-20120211
libapache2-mod-perl2 : Depends: apache2-api-20120211
Depends: libxslt1.1 (>= 1.1.25) but it is not installable
Depends: libmyodbc but it is not installable
Depends: xsltproc but it is not installable
Depends: libtimedate-perl but it is not installable

or

PLESK_ERROR: The apg-get failed with the following message: Reading package lists... Building dependency tree... Reading state information... You might want to run 'apt-get -f install' to correct these: The following packages have unmet dependencies: apache2 :
Depends: apache2-bin (= 2.4.18-2ubuntu3.9) but 2.4.18-2ubuntu3.8 is to be installed
Depends: apache2-data (= 2.4.18-2ubuntu3.9) but 2.4.18-2ubuntu3.8 is to be installed linux-image-virtual:
Depends: linux-image-4.4.0-128-generic but it is not going to be installed plesk-service-node-utilities:
Depends: libidn2-0 (>= 0.6) but it is not going to be installed

Cause

Non-standard repositories enabled in /etc/apt/sources.list file that Plesk is not compatible with, so a system cannot resolve all the dependencies properly.

Resolution

1. Connect to the server via SSH.
2. Replace all contents of the file /etc/apt/sources.list with the default content, like below:

   Default sources.list for Ubuntu 16.04 LTS:

   deb http://archive.ubuntu.com/ubuntu xenial main restricted universe
   deb http://archive.ubuntu.com/ubuntu xenial-updates main restricted universe
   deb http://security.ubuntu.com/ubuntu xenial-security main restricted universe multiverse
   deb http://archive.canonical.com/ubuntu xenial partner

   Default sources.list for Ubuntu 14.04 LTS:

   deb http://archive.ubuntu.com/ubuntu trusty main restricted universe
   deb http://archive.ubuntu.com/ubuntu trusty-updates main restricted universe
   deb http://security.ubuntu.com/ubuntu trusty-security main restricted universe multiverse
   deb http://archive.canonical.com/ubuntu trusty partner

   Default sources.list for Ubuntu 12.04.4 LTS:

   deb http://archive.ubuntu.com/ubuntu precise main restricted universe
   deb http://archive.ubuntu.com/ubuntu precise-updates main restricted universe
   deb http://security.ubuntu.com/ubuntu precise-security main restricted universe
   deb http://archive.canonical.com/ubuntu precise partner

   Default sources.list for Debian 7.x:

   deb http://ftp.debian.org/debian wheezy main contrib non-free
   deb http://security.debian.org wheezy/updates main contrib non-free

   or:

   deb http://security.debian.org/ wheezy/updates main contrib non-free 
   deb-src http://security.debian.org/ wheezy/updates main contrib non-free 

   Default sources.list for Debian 8.x:

   deb http://ftp.debian.org/debian jessie main contrib non-free
   deb http://ftp.debian.org/debian jessie-updates main contrib non-free
   deb http://security.debian.org jessie/updates main contrib non-free

3. Update package lists and install missing dependencies:

   # apt-get update
   # apt-get -f install

4. Run Plesk installation / update / upgrade.