As all Skype information is held in the cloud (Seattle) the best way to get a truculent installation working again is to completely uninstall the current version using the proper Uninstall routine.
Then download a reliable older version of Skype (7.37.0.103 is my favourite "oldie" available from filepuma.com) and install that as a clean new program. Run the program using your Skype name and password (you don't have to login to any Microsoft account) and voila! You should be back to your original profile with all your contacts waiting for your call. Using old versions will invoke the question "do you want to upgrade?" each time you log on but that question can be dismissed easily enough.
Once Skype is running go into the Tools section and under Options turn off "Automatic Update" to prevent the program reverting to the dreadful Ver8.
The "not supporting old versions" notice means that no tech support will be available after September but, like Windows XP et. seq. the programs will still run fine - just don't call MS tech support if you need any help.