I've had this problem for the past week. It seemed many people using Netflix had the same problem, which is where I found how to fix it as it applied to Sky Go too. Note: I am using Safari on Mac, so can only fix the problem for Safari.
For Safari users: Once Silverlight is installed, go to preferences in Safari. A smaller window should then pop up. Go to the security tab. Make sure Internet plug-ins is ticked to allow them to work. Then go to 'Plug in Settings' and make sure the Silverlight plug-in is ticked and therefore allowed to be able to work on the websites you want it to take effect, such as Sky Go.