You should repost this question under the other SNES category, maybe you’ll get some answers there. This model of the SNES doesn’t have an LED light because it is the cheaper budget version.
But my advice would be to first check the connection to the television. Are you using the composite (red-yellow-white) cable connection, or the RF (gray box with screw cable) connection? I have had RF connections go bad with my SNES that make it seem like it is not working.