After build 9860 for Windows 10 rolled out this week, some Technical Previewers reported that the modern version of Skype no longer functions correctly. The app will start to run, just never execute completely.
If you are having this issue, there's a fix supplied by Microsoft in the Windows 10 Technical Preview forums.
This is an issue with the Webcam Privacy settings in Build 9860. To work around the issue you will need to give Skype permission to use your webcam through "PC settings".
Close the Skype App
Launch "PC settings"
Locate Skype in the app list and move the slider to the "On" position
Remember, you WILL find bugs and be faced with problems running Windows 10 betas – so don't be surprised. At least in this case, there's a fix.