For non-home-cinema type situations then PowerDVD or WinDVD are often found bundled with DVD-ROM drives or can be bought off the web .. since this PC where it's not playing does have a DVD drive it may be worth you checking to see if it came with a DVD player package that just hasn't been installed.
PowerDVD can be found
here on Cyberlink's site, WinDVD is
here at InterVideo. There are several other players, TheaterTek is used a lot by home cinema owners but costs a bit more than these others and for home-video work is probably over-the-top, but I have no experience of those.
You can add just DVD decoders so you can use Media Player, such as
those from CinePlayer (which are the Sonic decoders used by TheaterTek).
Finally, there's a
freeware Media Player which I use a lot for MPG/AVI viewing, it also has some ability to play DVDs I believe (though I've never tried). It's small to download and simple to install, you may want to try that first of all.