This happened to me as well. I right clicked on the skype icon on my desktop and clicked on troubleshoot compatibility. I followed the prompts and was able to logon after this.
Hope this helps.
At the moment the quickest method to fix this is to install the beta version from here: http://skype.com/go/getskype-beta
Download and Reinstall the new Skype 5.7 beta version. See if it helps.
If not resolve this issue, then
Please do a Skype reset:
1. Ensure that "Show hidden files and folders" is switched on.
Click Start and then Run Type "control folders" and click OK. In the View tab, ensure that Show hidden files and folders is enabled
2. Exit Skype : From the system tray >> right click on the skype icon and click "Quit Skype"
3. Click Start >> Run Type: %appdata% Rename folder "Skype" to "Old_Skype"
4. Re-run Skype
Check if the issue persists
Location - Dhaka | Bangladesh - Standard Time Zone: GMT/UTC + 06:00 hour
If one of my replies has adequately addressed your issue, please click on the “Accept as Solution” button. If you found a post useful then please "Give Kudos" at the bottom of my post, so that this information can benefit others.