It's probably the TV. If you wanna check, just get a standalone DVD player if you got one, and hook it up to your TV. The problem is the resolution of a DVD is....480i. So if your TV is 1080p or 1080i, what the TV has to do is, for the lack of pixels of a DVD, it has to use more pixels, on the TV screen to fit it to the screen, so it'll do the same thing as if you're watching a lower quality video on your computer, make it full screen, it looks terrible.
I'd say your honest solution to this problem, find a regular TV, they're literally free by the side of the road now for quite nice CRT TVs, or if you buy one, like under $20 for any size you want at a thrift store, and just hoard them, as any old media you watch on a new TV is going to basically look stupid unless there's adaptations for it (ie, Dreamcast allows you to use a VGA adaptor.) Plus, despite sounding like an old man at age 20 like I always do, I like CRT as a technology. Inefficient, maybe, but it gives the most backlight, you never gotta worry about what angle you look at it, I overall love it, it's sad to see them go. However, once you get to bigger size CRT TVs, they're an absolute pain to move, which is the only practical reason I see besides a slight difference in power consumption (only LED and LCD) to go with LCDs, moving a giant CRT some place is no fun, and it's not space efficient in a room.