A few things to try here.
Try reinstalling your GPU drivers using the CLEAN method outlined in the drivers section here:
http://www.tomshardware.com/faq/id-2492424/laymans-simple-guide-solving-graphics-card-issues.html
Make sure you have all the current video codecs installed by installing the following codec pack:
http://www.windows8codecs.com/
Broswer settings might also affect video window green screen issues, so try the following. If you don't use internet explorer, most browsers should have a similar setting somewhere or Skype may have a hardware acceleration versus software rendering setting as well:
Try this guide:
a. Open Internet Explorer.
b. Click the Tools button or press Alt key + X, and then click Internet Options.
c. Click the Advanced tab, and then browse to the Accelerated graphics section.
d. Click to select the Use software rendering instead of GPU rendering check box.
e. Click Apply, and then click OK.
f. Close all open Internet Explorer window and then test the issue.
Lastly, make sure you have the most recent version of Skype installed. Make sure you uninstall all older Skype versions and reboot before upgrading to the new version for best results.