I have a Macbook Pro mid 2014 running OS X El Capitan and I also have a 3.5mm audio jack to component plug. I want to display my computer screen on my TV (which has component input) but all I have is the 3.5mm audio jack to component. I don't want to buy another cable and I don't want to by an Apple TV. So, can the Macbook Pro output video (I don't care what quality) through the 3.5mm audio jack port or is there any way to configure it so I can do this?
No. It's an audio port not an audio/video port.
Per the Apple Support site: Mac Basics: Ports on your Mac
HDMI and the Thunderbolt Ports will carry both digital video with audio, but your analog audio port (denoted by the headphone icon) will only carry audio.
Your option here is to get an HDMI to Composite adapter that will convert the digital video/audio signals to analog composite signals. There are different makes/manufacturers. You should pick one with good ratings and that is not too expensive.