ANSWER:
Well the obvious solution was to update back to Skype 7.5 and then DISABLE the Skype Update Service.
1. Link to download Skype 7.5 - the last working version
https://web.archive.org/web/20141213144457/http://download.skype.com/msi/SkypeSetup7.5.0.102.msi
if the link above is not working for some reason, try this link:
http://web.archive.org/web/form-submit.jsp?type=replay&url=http://download.skype.com/msi/SkypeSetup7.5.0.102.msi
Note that we had to use the only working link to download Skype 7.5 from Archive.org. This is because Skype Team did not want to make it easy for us - they have recently (Jul 2015) disabled all downloads of all previous older versions of Skype. So we had to dig through Archive.org. Here is an answer on how to find working download links of older versions of software using archive.org.
2. Uninstall your useless Skype 7.6 then install downloaded 7.5 MSI file
You need to uninstall Skype 7.6 first before trying to install that MSI file. If you do not remember your Skype password - in my case I was able to uninstall and reinstall older Skype and I did NOT need to re-enter my password - the newly installed Skype was automatically logged in. However, it never hurts to know your Skype password just in case :). So here is how to uninstall Skype 7.6 and downgrade to Skype 7.5:
- Go to "Start > Settings > Control Panel > Add or Remove programs"
- Find "Skype 7.6" and click "Remove"
- I was not restarting my PC, immediately after removing the 7.6 I've double clicked on the MSI file from Skype 7.5, and everything worked just fine
- after installing Skype 7.5, everything runs fine
3. Disable Skype Updater Service
Even that was not easy. Disabling it inside Skype Options was not enough, when I restarted the Skype asked me if I want to install updates (NO, thank you but NO) . So I had to dig deeper and disable Skype Updater
service as well. Here is step-by-step:
- Tools > Options > Advanced > Automatic Updates
- make sure that button label reads "Turn on automatic updates" which means the current state is OFF, i.e. Automatic Updates are disabled. Do not forget to click "Save" button if necessary!

- Goto Desktop > My Computer, right click on it, select 'Manage' menu
- Click on the "Services", look for 'Skype Updater' service

- right-click on 'Skype Updater' service, select Properties" menu item
- In the dialog window, select "Startup Type" to "Disabled", click "Apply", this would also stop the service

4. More Information