The only two reasons I can think of that something would play in black and white are:
(a) you are using an S-video connection and there's a problem with a connector or cable. If the connection is loose or broken, you can see an image but it will be black and white.
(b) viewing a PAL disc on a NTSC TV... I've not tried it but I thought that you can sometimes see the image but that it is black and white. There would be other problems with the image too, though, not just a lack of color.
What make and model of player are you using? What kind of TV? Are you using composite or s-video or component connection? Are you using DVD-Rs or something else (-RW, +R, +RW, dual layer)?
Seriously, I can think of no reason why it would display in color on your computer, but not on your TV.