|There must be a yellow RCA jack on the TV - that's for composite video.|
The video signal from the computer must go through circuitry that converts the computer's video output to the much older legacy TV display standards.
If the laptop has an "S-Video" jack, the circuitry that does that is already built into the laptop (the feature is called TV Out).
Does the laptop have a "S-Video" jack ?
If yes, you can buy, or you may already have been provided with, a standard S-Video (4 pins, male) to RCA jack (female)(gender) adapter - you simply connect that and use an RCA cable with male plugs on both ends to connect it to the yellow RCA jack on the TV.
Whatever type of adapter you use, don't expect much. Composite (or S-Video) video on the TV will not look anywhere near as good as the display on your computer monitor.
If you want the audio that goes along with the video from the computer to be coming from the TV's speakers, you need a 1/8" stereo plug (plugs into the headphones jack on the laptop) to a red and white RCA jack (gender) adapter and a pair of RCA cables with male plugs on both ends , or the equivalent of that (plugs into the red and white RCA jacks on the TV).