Please check the following:
Is the TV power ON?
Is the Nintendo Classic Mini power ON?
Is the bundled HDMI cable fully inserted into the system and TV?
Is it set to the correct TV input? Press the Switching Input button on the TV multiple times, and check if the screen is displayed properly (*1) (*2).
*1: Depending on your TV model, it may take a while before the screen is displayed properly. Please wait shortly after switching the input.
*2: Some TV models have a feature which will skip over any unused inputs for the sake of having smoother input switching. Please check whether or not the connected input terminal is being skipped over. See the manual for your TV for details.
If the above does not work, please try the following:
If the TV has multiple HDMI ports, try a different port.
If you have a different piece of HDMI compatible equipment, connect to that instead of the Nintendo Classic Mini, and check if it works.
Situation Not Resolved:
If the issue persists, please contact Nintendo Customer Service on (03) 9730-9822, between 9:00am to 5:00pm (AEST) Monday to Friday. For New Zealand consumers please call 0800 743 056.