Skype doesn't start anymore

As you can see here Microsoft decided to force people to upgrade to newer Skype versions and the old ones cease to work since a few weeks already. This might probably be related to Skype moving from peer-to-peer to being cloud based (mentioned by @Rsf).

As announced earlier this year, the old Skype for Linux v4.3 is at its end-of-life and will be decommissioned in the upcoming weeks.

You will be automatically signed out of Skype until you update. Please, update to the new Skype 8.x, which is ready for you with lots of improvements at Skype.com.

In case you hit any issues, please check known issues, system requirements, or post your questions directly to this forum. All your feedback will be greatly appreciated.

Kind regards,

The Skype Team
(source)

To get the newer version you should download the latest .deb file from Microsoft and install it with gdebi or dpkg (shouldn't make a difference but gdebi is a bit more secure when it comes to dependencies).

Be aware, the new Skype will create a file in /etc/apt/sources.list.d/ and will do so every time it updates if the file does not exist with the exact name Skype chosen for it. So renaming the file in /etc/apt/sources.list.d/ only calls for trouble in form of duplicated source list entries. You as well want to remove any before existing files for Skype in your sources.list.d directory.

You can rewrite the skype binary to present a different (false) version:

# perl -pi -e 's/4\.3\.0\.37/8.3.0.37/g' skype

and it works for now. Of course, it is just a matter of time till it stops working.