Update your flash player and try a different machine.. the hdmi port drivers on the computer may not be up to spec causing an hdcp handshake issue. Try updating your video drivers. It all works fine on my computer to tv setup.. I'm just saying it all works fine for me!
Restart the devices that you want to use with AirPlay or screen mirroring. If you're attempting to stream content to a device you set up in the Home app, check to make sure that Home Settings are not restricting AirPlay. Open the Home app, tap or click the More button, select Home Settings, then select Speakers & TV to adjust your Home Settings
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hbo on apple tv not working