Which example code are you using to test the Nunchucks? I'd suggest the nunchuck_demo sketch, which is an example included with the Nunchuck library. It doesn't depend on TV out at all, and it reports nunchuck data via the serial port. Are you using an official Nintendo nunchuck or a knock-off controller? What sort of data is printed out?
The tv out works, I get an image, I tried it with the serial port but, I still do not get anything (no numbers, nothing. The tx light on the arduino is not lit up). I'm using an official Nintendo nunchuck.
Please try the nunchuck_demo example sketch in the Nunchuck library. It doesn't product TV output, only serial port output. Be sure to set your serial console to 9600. It should produce some serial terminal output even if the nunchuck is not connected or not getting recognized properly. Let us know how it goes and we can help further.