A green screen during video playback could be caused by several different issues generally, depending on the source or where it is occuring.

The first thing to try would be a "Clean Install" of the latest video drivers, by choosing "Custom/Advanced" Install, and then checking "Perform a Clean Installation".

- If the green screen is generally only occuring during Flash videos, you will first want to try updating Adobe Flash.
You can also try disabling Hardware Acceleration. When in any Flash video, right click inside the flash player and go to settings. Click the Display tab (or Monitor Icon) and uncheck "Enable Hardware Acceleration" and close. Refresh the page (F5) and test again. Also see Adobe's Guide to Disable Hardware Acceleration.

- If the green screen occurs all the time or in multiple different scenarios, check your monitor cable. Oftentimes a faulty cable or bad connection could cause a green screen issue or green pixelation. Reseat the monitor cable and check the pins on the cable, if possible test with a different cable, test a different port on the card or different monitor to rule those out.

- If the green screen occurs in a specific media player or only in a specific format (.mkv .avi, etc), try testing in multiple different media players and different formats.
VLC media player would be recommended to test with as this has most codecs integrated. If it only occurs in certain players or formats it may be a codec issue, in which case you might want to try updating or trying a different codec pack.