You probably need to take a step back and better understand where you want to go and if what you have will work for you. In a more standard environment, your isp brings internet into your house and connects through a modem. From the modem there is a connection to a router. The router usually has 5 or so ports coming out of it that you can plug devices into like a pc, printer and a smart tv if the tv has an etherenet connection. The router is the central location from where all ethernet cables branch off.
From what has been mentioned, you have cables in the wiring closet that can handle ehternet - cat 5e but they look like they were set up for telephone. hard to see but looking at your patch panel it looks like there 4 screws per cable - a telephone 4 wire setup. Etherenet is an 8 wire setup and usually a sort of u shaped knife edge connector that the wire is punched down into.
As some mentioned, you can easily get a patch panel for ehternet that will fit in your closet.
But you need to know where the cables go from the closet to each of your rooms. This should have been done and labeled where you might have a wire number on each of the cables in the closet and the same number at the termination in each of the rooms. Similar to labeling circuit breakers in your electrical service panel. There are networking tools that can help you do this, but with a little more effort you can do this with a multimeter or voltmeter. You need to go to 1 of the rooms and tie 1 of the 4 twisted pairs together. maybe the room that the tv is in as a starting point. then go back to the closet and use the voltmeter to test conductivity across the same color of twisted pair. If you don't understand conductivity or how to use a voltmeter, spend some time in Wikipedia. You can get an adequate voltmeter from amazon for $10 -$20 and once you learn how to use it, you'll wonder how you ever got along without one.
Once you know which cable goes to your tv, you need to figure out how to get a cable from your router to your closet. Not enough info so far me to comment. But if it was my setup, I would connect from one of my router ports and used the prewired connection in that room to get to your wiring closet. Then add a switch. Connect the switch to each of your other remaining 9 cables. now you would have ethernet in every room of the house, not just where your tv is.
There really isn't anything magical about a prewired house. just a central place - your wiring closet, that has a cable running to each of the rooms - a hub. You need to figure out how to connect this hub to your router, then to your modem and to your isp for ethhernet.
Hope this helps. But you will probably need to do a bit more homework to figure it all out.