If you use Windows Media Player you may have to download some codecs because Windows does not come with them pre installed.
You can get K Lite codecs free from: http://www.codecguide.com/download_kl.htm
But I was still having problems with Windows MP even with K Lite codecs, so I downloaded the VLC Player in Igo's link and it works perfectly with all the DVDs that I wish to play.
How did you plan on getting another media player onto the computer?
Do you have a USB Memory Stick available?
You could try downloading the VLC player to a computer that is 'online', and save the download to the desktop. Then plug in the USB Stick and copy the downloaded installer to it. And use that to install it on the other PC.
In theory it should work.
Videolan is my preferred player; plays everything I chuck at it. It's not pretty like Windows Media Player, but I'm using it to watch movies, not wow at the semi transparent volume control or get frustrated with the Library