The reason you are running into issues streaming is because both the Chromebook Operating System and the streaming method you are using (PC to HDMI to TV) are not supported by the Slingbox. More than likely, the only reason you are able to stream on the Chromebook is because you are using the embedded Facebook player.
- Slingbox.com - What operating systems and processors are supported by Slingplayer for Desktop?
- Slingbox.com - How to watch your Slingbox on a TV
You can use any of the methods above and should have much better results.
I hope this helps!
Sling Media Technical Support