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Re: TV comes on but Roku menus do not always appear
What Roku device do you have connected to the TV? It appears your TV is coming on to the last used input. If that was Roku then the Roku menu comes up. If you push the home button instead of the power button on the Roku remote does the TV come on to the Roku menu?
If you want the Roku to automatically load up when you press the Power Key (or any other button on the Roku Remote for that matter), you need to verify that the Sony's HDMI CEC is "Enabled" and that Roku's "One Touch Play" is also Enabled.
To enable the Roku's One Touch Play feature (so any Roku remote button press will power on both your Roku and TV and automatically switch to the HDMI that Roku is assigned), using the Roku remote, navigate to Settings..System...Control Other Devices...and then select "Enable" (checkmark) for 1-touch play.
To disable the above, just Disable/unselect and the Roku will simply power on when Power button is pressed but will not automatically go the assigned HDMI. Your TV will simply be on the last HDMI you used (generally), or Antenna as the case may be.
The above assumes you have already programmed the Roku remote to work with both the Power and Volume Controls of your TV. (Settings..Remotes&Devices...Remotes..Set Up Remote for TV Control)
Hope that helps you.
Roku Community Streaming Expert Just another Roku user... I am not a Roku employee. Insigna RokuTV, Ultra 4660x, Premiere+ 3921, Express 4k+ 3941