I'm using cable boxes to HDTVs but the problem is likely similar. Have a 2 year Sony 34XBR910, straight DVI connection, has always worked fine. Have a 2 month old 30HS420, has HDMI input, when using a good quality dvi/hdmi cable the connection is lousy, have to jiggle the connection at the TV end to see a picture.....using component instead. My guess is that TV input connector is bad.
I just recently got the Sony 50" LCD RP and used a DVI cable to connect a DirecTV Hughes HTL-HD to it. I thought the PQ on non-HD channels was terrible, so I went back to component cable hook-up. Much, much better.
I used the DVI cable that came with the HTL-HD. It has digital-to-digital connectors on it. I don't know if a different cable with the combined digital and analog connector would work better or not.
The next time I upgrade my DVD player, I'll try the DVI connection with it.
Have a 42in Sony LCD. Had last years model, but had to exchange it. On last years model, using Monster DVI, I had frequent "snow" on HD channel if I stayed on the same channel for more than a few hours. I had to switch to another HD channel to get it to have a picture again. I assumed it was a software issue with the box.
On my new Sony LCD, I have the Monster DVI with a Monster HDMI adapter. No problems with picture quality at all, and no dropouts. Only complaint is that HDMI connections suck, they wobble easily, so I have it supported in the back by pushing the cable up for a tight connection, then duct tape to the back of entertainment center to keep it in position. I then used the duct tape to fix my car, put together a broken vase, and plug the hole in the local damn that was threatening to destroy an entire town.