A TV Tuner card will allow you to tune into terrestrial or cable channels on your computer. It won't relate to your Direct TV at all. Some tuner cards are capable of allowing a person to watch the encrypted cable package they subscribe to but this requires the use of a cablecard. Whether you can get one of those for this purpose from Direct TV is something you will have to ask them. Either way, a tuner will only provide you a direct television signal and antenna hookup to the PC it's installed in.
Testing your setup with a wire is only going to help if the connection between your machine and the wireless access point is the problem. If the problem is between the DVR and it's wireless access point, or a combination of yours and it's...