I have a Hauppauge WinTV-PCI card that's probably about 3 years old. I split my cable with a standard coax splitter and run one cable into my digital cable box, and the other into my tv tuner card. Using the WinTV software that came with the card, I can watch one channel on my TV and another on my PC.
However, my card cannot decode the digital portion of the signal. Therefore, channels that I can only recieve with digital cable won't work on my PC. I assume that all cable companies broadcast analog and digital signals together, like Time Warner does. When you subscribe to digital cable, you get a receiver box that can read the digital signal. The signal itself has been there all along though. So what you want to do is find a video/tv tuner card that has a digital receiver built in. Otherwise, you may only be able to watch analog cable channels on your PC.
There still may be another hurdle. Your cable company has to activate your digital cable box from their office. They can also deactivate it from there (if you haven't paid your bill, for example). This would likely mean that your digital tv tuner card would not have access to the digital cable signal without some action on your cable companies part, like leasing you a second digital cable box.