If I undersatnd your situation correctly, you do not have an "input" on your computer for the video/signal coming out of the Directv. Your computer has a video output only. The TV card won't help because it only has an RF input. I don't know if anyone makes a component to RF convertor, but even if they did, you probably woul dnot want it. RF is the lowest quaility - so you would be taking a high quality (SD or HD) signal and downgrading it to the lowest possible quality.
The only thing I can think of to do is to install a capture card as noted above. The Colossus is an internal card - but you need a PCIe slot for it. Does this computer not have any available expansion slots?
May I ask, why do you want to view in Media Center? If you don't want to record the program what benefit it is to watch in media Center rather than just watch it on the TV (or Monitor)? Is this computer a laptop?