It is very likely that your anti-virus may be the cause of YouTube videos not playing. To check if it is really the cause of the problem then temporarily disable the anti-virus and try playing the video. If it plays without any hassles then you can be sure that Kaspersky is causing the problem. You do no need to reinstall the application. This problem has been reported in many instances among users who have Kaspersky and Shield Defense. Both these anti-virus' are known to block YouTube videos from streaming. All you need to do is make these minor changes in Kaspersky:

Launch Kaspersky and click 'Web Anti-Virus' in the Protection section.

Click 'Configure'.

Click 'Customize' to make changes.

Click the 'General' tab.

Click 'Use streaming scan' and then click 'OK'.

Restart Google Chrome. You will see a defense warning on the screen.

Click 'Add to trusted zone'.

Click 'OK', once done.