The codecs that Windows Media Player can download and the klite codec pack are both for types of files (mpeg's and avi's) you would download. I thought you were saying that WMP will not play a DVD movie that you are attempting to play in your new DVD drive. For that you need a DVD decoder. I have never seen a free DVD decoder (I think there are royalties involved that prevent that).
You can easily determine if that is the case by downloading the free trial of WinDVD here:
http://www.intervideo.com/WinDVD/
that includes a DVD decoder. If that works, then you have to decide whether to buy a program such as WinDVD or buy a decoder that WMP can use.
What type of burning software do you have? Usually those software suites (whether it be Roxio or Nero) also include a DVD player that will have the decoder built in.