I had a similar problem a while ago with my TCL-Roku TV - sound but no picture. I don't know if it will work for Roku devices that attach to TV's.
- unplug the power chord to the TV
- press and hold the ON/OFF switch on the TV for 15-20 seconds
- plug in the TV power chord
- turn the TV on using the remote
Apparently there is a buildup of static electricity somewhere in the circuit. Pressing the ON/OFF switch, while not connected to power, drains this static and returns things back to normal.
It worked for me and I hope it will work for you.
Has anyone tried this on their Roku TV? As I said, the method WORKS, but I didn't see any posts about someone's experience with it. It really isn't that complicated.