You're probably seeing everything correctly, i.e. there's nothing wrong with your system.
There's several problems playing DVDs on computers:
1. Graphics card power has virtually nothing to do with playing a DVD. Doesn't really matter if you're using a 7800GTX or a TNT2, the graphics are displayed using overlay directly off of the DVD. The graphics card isn't using any processing power to alter the picture at all.
2. DVDs are stored at TV resolution, i.e. 720x480 NTSC (720x576 PAL), which is way less resolution than your monitor is capable of. When the picture is expanded to fill your monitor, the upscaling of resolution causes "jaggies" -- non-smooth diagonal lines.
3. DVD pictures are designed to be played back on a TV, which is an interlaced display device. Your computer monitor is not interlaced, it's progressive scan. To compensate for the difference, the DVD playback software deinterlaces the picture on playback. This loses some detail, giving the picture a soft, almost out-of-focus look.
4. Computer monitors have a brightness response (called gamma) that is different from a TV. This frequently results in the DVD looking too dark on the computer monitor.
5. Computer monitors have phosphors (on a CRT) or pixels (on an LCD) that have a much faster response (this is called less "persistence") than the phosphors on a TV. The slower response of the TV phosphors causes the TV fields & frames to blend together much more smoothly than on the computer monitor.
6. Because of the computer monitor's luminance accuracy, defects in the video from the DVD are much more visible. For example, all DVDs use compressed video, using MPEG-2. MPEG-2 compression can leave visible picture artifacts in some cases, such as blockiness, mosquito noise (where small pixels of noise surround high-contrast boundaries), and banding (where low-contrast areas look like they have bands of color instead of a smooth gradient). The TV's inaccuracies and slow phosphors smooth out these artifacts in most cases, but on the computer monitor they stand out like a sore thumb.
7. TV video color space and computer RGB color space are different. RGB can represent more colors than TV video can. This effect shows up on DVD playback as colors don't look as saturated as they should.
The combination of all of these effects renders DVDs looking like cr*p on computer monitors, especially LCDs. It can be mitigated somewhat (but not totally) by doing two things:
1. Using a software DVD player like the latest version of PowerDVD (retail), that has a few picture enhancement routines that can compensate for the gamma and color saturation. Your free DVD player that came with your Asus motherboard doesn't have these enhancements.
2. Calibrate your LCD monitor with a hardware calibration unit like the Monaco Optix XR.
Even with that, however, you'll never get video on the computer to look like it looks on a good television. DVD playback was designed for television, that's where it's going to look best.
In my company we do video editing and DVD production. Our video editing workstations have real studio-quality TVs hooked up to them -- we never trust what is seen on the computer monitor. The TVs will always outperform the computer monitors when it comes to video.