John McGaw
OK. So your TV is being fed by a ROKU box which is wired to your home Ethernet connection. No help there for feeding the TV from the computer. The easy answer (for me at least) is to say that it is often possible to feed video HDMI cabling at a 50-foot distance. I qualified that with 'often' because it will depend on the quality of the cable and connectors and 50 feet is legitimately more than one expects to work perfectly in the majority of cases. That would mean that using the HDMI output on your computer (most newer video cards are so equipped) and feeding a second HDMI input on the TV might just work.

As for recording YouTube videos to DVD, if you do a search online for something like 'capture youtube video' you will find many solutions. If you can capture it in some form then burning a DVD is usually a simple matter if you have the proper softare. I used NERO but there are free programs that purport to do the job too.