A video card doesn't detect a TV. 'Detection' is called EDID and requires a specific wiring connection only found on more advanced displays. This means that what your card IS detecting is you using a non-standard connector type.
You can't set the resolution for any video to a display using single composite RCA (yellow) connectors. It supports one, and only one, resolution: 480i.
While I'm not a specialist with that card, you should be able to go into the card settings and you will set it up to output composite video. By default, it likely sets up for component (red/green/blue) video. Component video also uses RCA connectors, so saying "RCA" doesn't specify the exact connection used, but my expectation is that you only have that single yellow RCA input, which is called composite video. You need to figure out, with the graphics card, exactly how to send composite video to your TV, and that would be in the settings of the card.
Make sure, as well, that you are using the correct wire of the three wires for the composite video connection. As well, make sure the video card actually supports what you are trying to do. I have an inexpensive video card on my PC and it still shipped with a separate, and specific, video breakout cable to connect to my TV if I needed to.
If nothing else works, you could make that leap into the new millenium with a flat panel TV.
EDIT: What makes this much more difficult is that the nVidia card is actually a chip set used by many manufacturers so you haven't been nearly specific enough about the exact video card you have purchased. If you can provide a link to Newegg.com or Amazon with an exact model, perhaps you can get some specific instructions on what you want to do.
For example, this version of the card ($42) comes with the breakout cable that you specifically need...
http://www.newegg.com/Product/Product.aspx?Item=N82E16814139018&cm_re=nvidia_geforce_8400_gs-_-14-139-018-_-Product
It would be incorrect to assume that because your old card did it, a new one would as well by default. Most people, these days, hook up their PC to their TV using a HDMI, DVI, or VGA connection for best possible quality. Composite video is VERY low resolution, and may be supported less and less by newer video cards. Especially cheaper cards. Just something to consider that it may not work at all.