It could be that the output resolution from the DVR box is set to 480 or a lower resolution. Have you checked the output in the DVR's menu? The logic board - as far as I know - wouldn't be the cause of this.
I have a 40 inch Samsung TV which I've had about 3 years (sorry I Don't have the model number handy). I have DirectTV and an HD-DVR. The HD Channels were great up until about a few weeks ago. Now sometimes (not all the time) even the HD Channels look very grainy and fuzzy, much they same way they did before I got the HD Reciever/DVR. I'm trying to figure out if this is a DirectTV problem, or a problem with my TV (or maybe just a bad cable).
Interestingly enough, about 4 or 5 months ago, the logic board had to be replaced in the TV. It took almost 20 minutes some mornings just to get it turned on. Best Buy came out and replaced the Logic Board and all was fine up until about 3 weeks ago. I'm not sure whether to go to Best Buy for help or DirectTV.