This is similar to the problem Im having; yes you CAN connect the directtv and run it on the monitor, for this you basically only need a video to USB adapter, these cost about $40 (cheapest) to maybe $80 for a decent one?
The output of the directv or dvd or vcr includes the rca-type connectors for Video, (yellow colored) Audio-Left and Audio-Right (red colored). Left is white; dont confuse these for the RGB or Component rca-connectors, the colors are put there for a reason, not to be colorful.
you can connect up the video/audio to the usb adapter thing, and with software it can import and stream the video to the screen of your PC.
The better solution is to get an All-In-Wonder video board but make SURE the box you get at the store has the rca-connectors with it! or you will have an AIW in the PC with no way to connect up a directv or vcr. (and then be in a similar boat that Im in)
others can comment about gold plated rca-cables working better or being the same but if possible get gold plated ones