Ok, going to try this again, perhaps with a little different style of posting.
Paul's right on the money. Only other thing I could think of that could be a possibility is it could be a non reception related issue involved with processing of the video signal being done "by the set", so to speak -- could even be something specific to the DVI connection - If so, you might want to check "hardware" and display areas at AVSforum and see if you can find anyone else having the issue with your set or the LST3510 and DVI. [update: You might also want to try using component video connection from STB to set, and/or try adjusting EE or "sharpness" setting to see if that does anything].
If it's a reception related issue, the signal has to be extremely "marginal" condition for the decoder to have such a hard time at it, and, there should also be other indications reception issues are involved -- It's usually very unusual to have such a marginal signal conditions without also experiening on screen data loss(usually shows up as "green" blocks for the missing data) as well frequent dropouts(both audio and video simultanously), or "low" or "bouncing around" reading on the receiver's signal quality meter -- For instance, if the "lowest" readings are at/below/around the readings which are required to just barely be at the "threshold", or "on the edge of the cliff" for reception correspond with when you see loss of data/pixelization or have audio/video dropouts - then it's a reception related issue.
In order to receive the digital/HD stations by hooking up the antenna to your display, the display has to have a built-in ATSC tuner (otherwise you'll just get the analog stations) -- If your set has one of those, might be a good idea to try it and see if the problem you're seeing go away. if It does go away, and it isn't because its tuner is a little better sensitivity/selectivity wise, or at handling multipath(reception issues) then the LG STB, then there's something going on that's probably specific to DVI input on your set, or the DVI output of your receiver ... Again, probably best to see to see if you can find any posts in hardware or display area about the issue with your STB and/or display model, in case others have ran across it as well and how they were able to fix it.
You need to hook up an OTA antenna to the 811 in order to receive the HD/digital local stations. They aren't available currently via the dish/dish locals package, you can only get the "old fashioned" analog stations(but converted to SD digital by dish network) that way. For more info on OTA antennas, you might want to start out at the OTA antenna FAQ in hardware area, here :http://www.avsforum.com/avs-vb/showthread.php?t=611957