HDTVs are no longer made with a CableCARD slot, If you purchased an old one that did have a CableCARD slot, it would not work anyway because Cox uses SDV (Switched Digital Video), and HDTVs never supported SDV Tuning Adapters.
A TiVo will NOT work without service. You could purchase a used one that already has Lifetime Service for about $300-$400, maybe even cheaper on ebay. The Roamio is the current model, a Premiere would be the last model, and a TiVoHD is the prior model. (only the Premiere and Roamio support the Contour HD Channels which are MPEG4/H.264)
For a simple one tuner HD CableCARD Set-top-box there is the Samsung GX-SM530CF Cable Box it does support SDV.
http://www.amazon.com/Samsung-GX-SM530CF-Streaming-Player-Built-In/dp/B00EYO241Q/
You could also get an SiliconDust HDHomeRun PRIME connected to your network and Win7 PC and then get an XBox or Ceton Echo for the HDTV Set-top-box.
http://www.amazon.com/SiliconDust-HDHomeRun-CableCard-3-Tuner-HDHR3-CC/dp/B004HKIB6E/
http://www.amazon.com/Ceton-Echo-Windows-Center-Extender/dp/B008TZJ126/
The SD HomeRun PRIME is also DLNA Certified and the Samsung SmartTVs have an App to Stream directly from the tuners without a Set-top-box. It is not very elegant but it works.
http://www.samsung.com/us/appstore/app.do?appId=G00010110215
The Tune N’ View app for Google TV supports direct streaming from HDHomeRun devices on compatible Google TV devices.
http://www.silicondust.com/products/hdhomerun/prime/
CableCARD and Retail Devices - Support
CableCARD FAQs - Support