At best, the resolution of the content of the DVD is 720x480. Your trying to stretch that resolution to fit a 1920x1200 (or 1920x1080) screen. Some graphic cards will attempt to upscale the resolution of the DVD content so it doesn't look as bad on larger resolution monitors.
Here's a simple test. Start playing a DVD using whatever software you're using in a window. Resize the window to about 1/4 the size of your screen. Does the image look better?
If so, then you could probably do better with a low-end graphics card, like this ATI HD 4350
from Newegg for $30 ($15 after MIR).
Quote from ATI's website concerning the HD4350:
The ATI Radeon™ HD 4350 GPUs can upscale video on displays up to 1920x1200.