You could get some kind of mini pc, old laptop, buy a used pc, whatever, and plug it in with HDMI into the TV just like you would a monitor. Get a wireless keyboard and mouse, or setup an xbox controller to control the cursor, or just get a trackball and map an extra button to activate an on screen keyboard. Load Plex up onto the computer however you do that, and then browse your collection from the couch. It would take some legwork and maybe there are tools to help you set it up but just research and take your time, you can do it.
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