I feel a little bit stupid now.. I told my friend about the problem and he said "There is audio and video output on the side of the nintendo".. and yes.. there is. I have always looked only the backside, which has the RF ouput, but there are two RCA outputs on the side with labels "audio" and "video".
So, problem solved. My friend lent me a cable also. Now I can play Super Mario on my new 50" tv.
BTW.. super bowl half-time show was horrible.. where are the real superstars! I need to watch Micheal Jackson, Rolling Stones and Prince on youtube to compensate my disappointment.