Are you sure it was component and not composite? If it is component(usually for HD) just run 5 runs of rg6(3 for video and 2 for sound)mark them accordingly and buy the rg6 RCA male connectors to put on the ends,if it is composite ,run 3 rg6 cables(1 for video,and 2 for sound)this will be way better than using a monster cable or other junk they try to sell you ,and easier to pass as you can pass one at a time without the connector on it.

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Your new TV has three (3) HDMI inputs, one composite or component input, and an coax input. In other words you have two (2) non-HDMI inputs. I'm assuming you want to use the DVR recorder to record shows from the Dish DVR??? Then the connection would be Dish DVR ==> DVR Recorder ===> TV. If the DVR recorder has a component output, then I would use that to connect to the TV. If not, then you can use the composite connection or the coax connection, using the remaining input for the VCR. You might want to think about upgrading to a HD box from Dish to take advantage of your new television. There is quite a difference between standard definition and high definition.

I like the look of your room. You could keep the coffee table you have (unless you want the shelf for function) and bring in some wood with a new console. (Can't see how much space you have or what functions you need, so just some guesses...)https://www.houzz.com/products/four-hands-irish-coast-tv-console-prvw-vr~41837930 https://www.houzz.com/products/modern-craftsman-3-piece-entertainment-center-distressed-oak-prvw-vr~28651590 https://www.houzz.com/products/64-contemporary-rustic-tv-stand-media-console-prvw-vr~53813700 https://www.houzz.com/products/70-wood-tv-standdriftwood-prvw-vr~23682205 Otherwise, you could go a number of directions with your decor... https://www.houzz.com/products/mercer-tv-stand-white-prvw-vr~68481857 https://www.houzz.com/products/melange-raellen-console-prvw-vr~24963556 https://www.houzz.com/products/60-tv-stand-gray-prvw-vr~77608987 https://www.houzz.com/products/art-home-furnishings-chateaux-entertainment-console-grey-prvw-vr~22976463 https://www.houzz.com/products/walker-edison-52-wood-console-table-buffet-tv-stand-antique-gray-prvw-vr~91755154 Hope this gives you some useful ideas, anyway. Obviously just guessing at what you might like in terms of style and interest. Closed storage definitely helps keep things tidy though!