I know there is a LOT of information regarding this issue as many people have run into it when they used it before or with a brand new Acer C7 chromebook.
If your Chromebook is not working with your TV, first try another cable.
If it is still not working then try it on another TV or monitor with HDMI input.
The previous step is kind of mute, although it will assure you that the issue is not with the chromebook, but with the TV itself.
However, if it does not work on another TV or monitor then you need to simply "Reset Default Settings" or do a "Powerwash"<--(which will erase everything stored ON the chromebook, cloud saves are not affected).
There are many different ways to reset certain settings within your TV that have to due with the HDMI ports. Just do a quick search for how to reset HDMI ports or even the HDMI settings pertaining to your TV manufacturer.
For Samsung(My TV) it is as simple as removing all HDMI cables from the TV and then unplugging the TV from the wall for at least 10 minutes.
Once I did this I was immediately able to watch YouTube videos again on my big screen with no lag!
I hope this helps others that have run into this issue. Cheers