A couple of things:
1) If you have cable or a dish, you need to make sure that you have the right equipment (with Direct TV, that will probably mean a new dish and new receiver). DON'T make them charge you for it....they probably will try. Threaten to change to Dish Network if you have to, but its stupid to pay for the upgrade. Around here, they charge you for it, unless you bitch.
2) With most cable companies, you need to have them turn on the HD service. Ours is free (although I get the tier programs), but yours might be different with the dish.
3) HD channels with cable companies are usually NOT the same number as the regular channels. With our Time Warner, all the HD channels are in the 600's. Check where they are with Direct TV.
4) A lot of standard def TV looks like shit on an HD set. You'll eventually giving up watching anything that's not HD.
5) Make sure that when you watch standard channels your set is not "stretching" the picture to fill. You should get black bars on the left and right. Stretching to fill will just make a bad picture worse.
If the TV looks good for the XBox, its likely a problem with the cable/satellite and not the TV.
TBW