I have a box currently set up near the computer so that isn't an issue, but I need a capture card rather than a tv tuner?
That's the ONLY way you're going to get a video feed from your box to your PC. Keep in mind that some of the channels are also going to use content protection (such as HBO in particular, etc), so they will block the video capture card from getting the signal.
To be honest, you'd be better off just getting a cheap 24" or 32" LCD TV (they could be had for about $150-200 now) instead of a $100 PVR card that isn't going to do you any good, set it on your desk next to your current monitor, use one of the inputs for your PC as a second monitor and one input for your DirecTV box, and just swap inputs for when you want to watch TV.
Your ONLY other option is going to be DirecTV Everywhere... but that's basically like Video on Demand. It won't let you watch live content, and it will only stream either what you have recorded on your DVR (if you have one) or download from the Video on Demand library for the channels you have access to. Last time I checked, it's MOSTLY premium channels like HBO, etc.