The different color inputs and outputs on video equipment represent different video quality. The Red, Green, Blue (Component Video) will have a much better picture quality then Yellow(Composite Video) with the Red and White (Audio). These are "analog" connections. There are also "digital" connections for video and audio. There is HDMI and DVI for video and Optical and Coaxial for audio, to name a few. Here's a link showing the different connections.
http://www.hometheatermag.com/hookmeup/1105hook/
Let's start from scratch. Disconnect everthing from the TV, including the DVD player. On the back of the TV is a HDMI input. The HR21-700 DVR has a HDMI output. Connect the two units together with a HDMI cable like the one posted by Sonnie above. Once you get everthing working fine with the HR21-700 DVR and the TV we'll move on to the DVD player. On that note, what is the make and model of the DVD player, as some have both digital and analog connections. Knowing what you have will make it easier to recommend the setup.