Before going back to the store to return my set, I called Roku Support. The young lady talked me through the solution:
- Pull the power plug to the TV
- Hold the ON/OFF button on the TV for 15 seconds
- Plug the power back in
- Turn the TV on using the remote
SUCCESS! Everything returned to normal (except that darn NEW Guide).
It seems that this drains the excess of electricity that builds up over time and then interferes with the electronics of the set.