If the computer has no specific selection for color space or video sync. and no separate video output labeled "component" then the output video format in terms of color space is RGBHV that is, RGB with separate horizontal and vertical sync.
If the TV has no VGA jack and no specific selection for RGB/component video via a component video input, then it expects just Y/Pb/Pr component video and with the sync. combined with the Y.
Check the instruction manuals to be sure.
If the computer and TV have no video format in common (probable) then you need the transcoder.