Reply to Comment
I appreciate all the cable company employees who weighed in here and gave us some facts. That helps with my perspective.
However, I feel I have DEFEATED THE EVIL!
I bought a Samsung SmartTV. We still get cable through our CableCARD on the original LG, and it still freezes up from time to time. I now believe the problem is in the CableCARD itself, as I've replaced the other two main components and seen the same issues. We also don't have freezing when I use HDMI input directly from a computer.
The Samsung SmartTV is connected to the internet, so I get NetFlix and Amazon Direct, which is the majority of my viewing. It also has the XBox360, so I'm good with DVDs. The thing that finished it off, however, was adding a terrestrial antenna. I now get CBS, NBC, ABC, PBS, and several other local channels. If there is something I want to watch on network, the antenna brings it in in HD. Very cool.
We'll still watch cable on the LG, though.