Just so we're all on the same page, your cable card (CC) looks like a thick metal credit card and goes in the slot on the HD HomeRun Prime. This is required in order to tune all your subscribed channels. There is no other card involved (Digital Card?). The Tuning Adapter (TA) is another box that looks a bit like a modem. It's also required if you want to get all your subscribed channels and your cable systems uses something called Switched Digital Video (SDV). Cable systems with several hundred channels can't fit them all on the wire going to your house. So many systems have adopted SDV to solve this problem. When you tune a channel, the request goes to the TA which in turn asks the cable company to put your channel in the stream. If you don't use a TA in an SDV system, you'll still get a lot of basic channels but will be missing several others. Without your own TA, the SDV channels you do get will depend on whether someone else in your neighborhood is watch them as well.
If I were you, I wouldn't let Cox or SD off the hook until you got all your channels.