As a guess, during the HDMI handshake in which the Roku and TV exchange information about capabilities, the Roku is interpreting feedback from the TV as saying the TV supports a resolution (4K maybe) that the TV doesn't actually support. So after the startup when the Roku switches its output to that unsupported resolution, the TV can't display it.
I'd suggest trying the Roku on another TV where things are working. If it comes up okay, go into Settings > Display type and change the Roku to the actual resolution of the problem set instead of the "auto" setting. When you get to the countdown screen click on the "yes" option. Now move the Roku back to the first set and see if it works.
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