Any computer output to an old NTSC screen (which is what it sounds like you are using) is going to look like crap and be limited to an 800 x 600 display. Which means you may have to change your monitor to display 800 x 600 too, and you will lose a lot of display area, thus defeating the whole point of plugging in the TV.
It used to be common to find video cards with S-VHS outputs on them, where you could easy install an adaptor to convert the S-Video to the single RCA video & audio that your TV has. But these are going away as old NTSC analog TVs disappear and are replaced with digital flat-screen TVs with 15 pin video ports.
While I understand what you are trying to do, honestly the best thing would be to just forget about using the TV. The display will suck and its just not worth it. Once you replace the TV with a digital flat screen, then yes by all means.