Best bet is to take the NES Console apart, neatly and replace the 72-Pin connector. This will solve the problem 99.99% of the time.

It sounds like your A/V Cable is DOA, or your A/V port is either DOA or dirty. Take 91% or higher rubbing alcohol and put some in a spray bottle spray the cord just a little on its connectors, and spray the A/V port just a little. Tilt your console back on the ports and sit it against something solid like a cabinet. Let the rubbing alcohol flush the ports and dry (takes less than 5 minutes). Then plug the cable into the port and make sure your TV is on its A/V channel. That should solve your issue.

It is like Taylor Said ^ It was meant for a CD Expansion, or the Stellaview same reason most Nintendo Consoles have the same port except it was only really released in Japan and are extremely expensive. It was also meant for Nintendo Test Stations, since the disc drive nor Stellaview were released in the U.S. it's primary function became for the Nintendo Diagnostic/Test Stations. They originally were working with Sony to produce a console that would utilize both cartridge and disc games, however when Nintendo decided to work with Phillips, for reasons that I will not go into detail for, they breached Sony's contract. Sony then later released the PlayStation with the slogan "PlayStation, It Only Does Everything!" it is also the same reason why some PlayStation commercials began with the commercials for Sega and Nintendo and led into theirs, that way they were able to show the consumer that they are better than Nintendo and SEGA.