I hate to repeat myself but here it is.
With that said, you are correct assuming you had a display that didn't give the maximum display quality potential before replacing it with a better TV. With, say an HD TV, you are now surpassing the quality capability of the DVD so now your bottleneck in quality will be either the media itself or the DVD player. The DVD player in my current situation is my bottleneck. I have had my surround sound system and DVD player for over 8 years and at the time HDMI was not common place. I am stuck with component cables to give me the best possible display quality out of that DVD player. There is a huge difference when watching a DVD on my player versus watching an HD channel through my DVR box through my cable provider. I currently own a Samsung 50" LED HDTV 1080p. I don't remember the model number off hand so I won't provide a link to the TV in case it's the incorrect model but I've thoroughly enjoyed this television. The TV itself is normally around $1,100 to $1,200 but I found it on sale a few months ago for $800 at Sears and Walmart. I tried to look for the same kind of deal just now with no luck. The prices have shot back up on all of the similar televisions.