Please check the following.
There may be a possibility that the Auto-Shutdown feature had turned the power OFF.
Turn the switch OFF, then turn it ON again.
Is enough power being supplied?
Make sure you have a USB-compatible AC adapter that can supply 5V-1.0A/5W or more of power (or equivalent to USB 3.0), or equipment with a USB connector such as a TV or computer. Then, connect it with the bundled USB cable.
Also, if there is a separate piece of equipment with a USB connector that is supplying power, check that the power supply of the equipment that is connected with the USB cable is turned on.
Is the bundled HDMI cable fully inserted into the system and TV?
Make sure it is fully inserted into both the system and TV.
Does the external input of the TV have the correct settings?
Press the Switching Input button on the TV multiple times, and check if the screen is displayed properly.
* Depending on your TV model, it may take a while before the screen is displayed properly. Please wait shortly after switching the input.
* 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 of your TV for details.
Situation Not Resolved:
If the issue persists, please contact Nintendo Consumer Support on (03) 9730-9822, between 9:00am to 5:00pm (AEST) Monday to Friday. For New Zealand consumers please call 0800 743 056.