The Coby is not a 'surround sound system'. That's important to understand. There are basically no integrated DVD (or Blu-ray) players which have built in amplification and a proprietary speaker connection system which can act as proper surround sound systems.
That said, if you have it, and it works, AND your TV has analog audio output, like a headphone jack connection, then you can connect the TV to the Coby using those connections.
Now, you should look at the manual for the Coby as it shows the different connections.
https://www.manualslib.com/manual/394172/Coby-Dvd-937.html?page=12#manual
It's important in AV to know the difference between an INPUT and an OUTPUT. Outputs come from source which produce audio or video (or both). So, a cable box, a laptop, a game system, and other playback devices have audio and video outputs. Usually HDMI these days, but sometimes you get analog audio (red/white RCA connections) or digital audio (fiber or coaxial).
The TV you have has a mix of inputs and outputs. The HDMI connections are ALL INPUTS - with one note, the ARC connection is the TVs ability to send audio back to a modern A/V receiver which also has ARC capability. The Ethernet connection is for your home network and is a two-way network connection for data. The F-connector (cable antenna) is an input that feeds cable television or over-the-air broadcasts. The optical out is an audio only connection which is the best and most convenient way to get audio out of the TV in the highest quality that the TV allows. USB is typically for memory cards with some videos or audio files on it that are compatible with that specific TV (not all TVs handle the same stuff, read your manual, and cross your fingers if you plug in a USB drive). The AV-in adapter typically has a separate cable that came with the TV which allows connections to legacy analog gear. Like your Coby has a yellow composite video output, a round S-video output, and red/green/blue RCA component video outputs. Those could be connected to the AV-in connection on the TV using the adapter that shipped with the TV.
For your Coby and the TV that you have, there is no question to me that the least expensive solution is to get a headphone to RCA adapter cable. Many TVs these days do not have a headphone output on them, so you may want to plug in some headphones first and make sure you get good audio out of that connection. If you do, then just run audio down from the TV to the Coby using the proper headphone to stereo RCA audio cable.
BEFORE YOU BUY AGAIN: Setup a budget, ask questions, look around. People here are happy to help you make rational decisions on ways to spend your money. Yes, $20 isn't a lot of cash, but if you actually are on a budget and want decent sound, you may find a decent surround receiver that is a few years old for under $100. Maybe a lot less as some older receivers can't handle HDMI and while they still make good audio, they make lousy modern receivers (optical out from the TV to your receiver for good surround sound!).
Speakers are a different story. Good speakers are good speakers are good speakers. They don't lose their value and they cost money. But, inexpensive speaker setups can be had as well. So, ask, and do some shopping. I use a $50 set of speakers in my basement right now. They work nicely for a room which has kids shooting bows and arrows around.
