I recently bought a wireless Roku and also bought the Roku Ultra which let me connect via Ethernet. Everything works except when I turn the Ultra back on. The power button on the remote will shut off the TV and Roku. When I turn it back on, just the TV turns on. I need to press the button on the Roku to turn it on. It's not the worst thing but something that I'd like to fix.
Pressing a Roku button on the remote such as Home should wake it up.
Rokus have never turned off and on. However, recent models do "go to sleep" (have a reduced power mode) after a period of inactivity. You can turn this feature off if you like. It's a little confusing because the power button has always been for the TV only. And no one thought about it before, because Rokus never used to go to sleep, so you would turn on the TV and see the Roku (because it never turned off).
So, after I turn my TV on, and set it to the Roku input (if needed) then I press the Home key on the Roku to wake it up.
Then again, Rokus only use about 2 watts when idling, so some people think the low power mode isn't worth the bother and turn it off.
Oh, and if you're looking at the light on the Roku as an indication of "power", the behavior of that light is actually kind of complex and doesn't really map to power being on or off.