WOW! Glad I found this thread. This happened once before to us when we were in the first week of owning the R3. No idea why, but even cable/dvr would not work. unplugged power to everything (tv, cable/dvr, roku) and then plugged them all back in and everything was fine. Unexplained.
Then it happened again today. The HDMI switcher is my tv - I plug my cable box/dvr into the TV with HDMI cable, R3 into the TV with an HDMI cable, BluRay player into the TV with HDMI, and Wii with regular rca plugs (yellow, red, white). I turned on the TV and the kids had been playing Wii earlier and left it on. I turned off the Wii and switched the TV to cable box/dvr and got nothing but a big green screen. I switched to the R3 and it was in its normal screensaver mode with ROKU on the screen in different places. I went in the R3 to amazon prime, picked a movie and started to watch it, but when the movie starts, I get the message "hdcp unathorized access, content disabled". I tried other (HD) movies - same thing. R3 menu is fine, playing (HD) movies is not.
To fix it, I powered off the TV (waited 10 seconds until I heard the internal click of it really shutting off) and then turned it back on. I went to cable/dvr and everything was fine (1080i). I switched to R3 and it was fine, but detected 720. I went into the R3 settings and it was set to 720. I put it back to 1080, switched to cable and then back to R3 and it recognized 1080. Everythign is OK now.
So, for me - it seems to get messed up when we switch the TV to Wii and then back to R3 (or to AVI input, then back to HDMI input). I assume Wii plugged into AVI input does something to put the TV into a less than 1080 state, and switching to R3 or cable box as 1080 whacks it out. True powercycling (wait until it is really off or unplug the power cord for 10 secs) of the TV fixes it for me. I need to make sure the Wii and TV are both turned off before trying to go back to a 1080 source.