Uninstall the currently installed version the temporarily revert to version 184.108.40.206. Based from what I read from the posts of experts from this forum, it seems that there are some bugs in the latest version (6.3). You can download the installer from the link below.
You can just update your Skype software again once Skype release a fix or a new update.
Also, what is the version of Internet Explorer installed on your computer?
In Internet Explorer go to Help -> About Internet Explorer.
What do you see when you open this link in your Internet Explorer?
P.S. Please, don’t say that you are not using Internet Explorer. This is irrelevant. Skype depends on Internet Explorer.