If your TV has the message "no connection", that sounds like the TV is generating the warning and the first thing to check is whether you have the correct HDMI input selected for where your TiVo is connected.
Having said that, your TiVo should have lights on the front-left. From L-R, you have 3 green LEDs. First one is power which should be red in standby, green when on. Second is the online light representing the internal 'net connection. Third is the remote input.
What are you seeing? You can also try pressing the "power" button on the front-middle of the TiVo rather than on the remote, if necessary.
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