You may want to check out avsforum.com for answers to your HDTV questions. I have gotten great advice and information on their site.
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Add a few hundred and you can get a JVC 52" LCoS. I am happy with mine. The newer model looks even better and has the built in tuner and cable card you are looking for.
Better: add a few hundred more to that, and get the Sony 50" LCD rear projector.
Best Option and IMO, the best TV, is the Sony XBR LCoS but, you'll need to nearly double your budget.
If you are okay with a big box 160+pounds and large footprint check out
I bought this tv just before they added the cable card slot & tuner and it is a very nice television for the money. The picture quality is great but it is large and doesn't hang on the wall like a plasma or other slim tv. For your price range I don't know if you could beat it. They did have a 51" model but the link above is for the 57" like mine. Good luck.