The Power button and the Volume buttons on your Roku remote are "TV Controls". They only interact with your TV, they do not interact with the Roku device. (Only RokuTVs and Streambars will stop streaming and turn off when Power button is pressed - all other Roku devices need to be returned to Home Screen to stop streaming).
When you are finished streaming, you need to press the Home button on your Roku remote to return to the Roku Home Screen. (this will stop all streaming activity and data usage). After a while, the Roku device will enter a Sleep Mode. (light should go off when it does).
When you want to use the Roku device again, you will need to press the Home button on the Roku remote to "wake up" the Roku device. (light should go on).
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You can also try enabling Roku's 1-touch play (a CEC feature). After you enable CEC on your TV under the TV settings (using your TV remote, not Roku remote) under the HDMI settings, you go into your Roku Settings/System/Control other Devices/1-touch play [checkmark to Enable].
With 1-touch enabled, and your TV's CEC enabled. you should be able to press any button on your Roku remote (excluding the power and volume keys). and simultaneously the TV should power on, the HDMI automatically switch to the Roku, and the Roku device should be awakened. You will then find yourself on the Home Screen.
Again, when finished streaming, press the Home button to return to Home Screen, then Power button to turn off the TV.
