On your desktop, you may have software like nvidia purevideo, PowerDVD or WinDVD which would allow Windows Media Player to decode DVD video (some programs also include their own player software). This is what Windows means by the decoder, which you don't appear to have on the laptop.
Rather than waste good beer money, I suggest you try VLC Media Player. It's free and will play anything you throw at it, including DVDs
. You can get it at
http://www.videolan.org.