This might be related to the game, so what game is that? It looks 2D, and that brings with it a high probability of there just being a problem with the bitmaps (or whatever) that are in the game. Honestly the roughness of that black line looks pretty jpegy. A LOT of 2D games suffer from all sorts of problems with compression, fake low res, conversion, etc. I'll check too, if I have the game. I don't use LCD TVs, but I have a monitor I can check it with.
There is (almost) certainly no problem with the VGA box since the DC puts out VGA natively, but the signal is 640x480. Is your "HDTV" an LCD? If so, can you display the image not scaled in any way? If it is being stretched to fill the horizontal height then this could also be an artifact inherent to the scaling hardware of your TV.