Problem is you've got a composite cable (the yellow RCA jack) plugged into one of the inputs for your television's component connection (Red, Green, Blue). It's really odd that you seem sure that your TV has no green input since a component connection is usually all three.
Composite cables (just a yellow jack) have all video information going through one cable, which requires a lot of compression and the result is poor video quality. A component cable (Red, Green, Blue) have more bandwidth, three cables to carry all the video information. One cable carries the luminance information (black and white brightness information), the two others carry the chrominance (color) information. So most likely the reason you're getting just black and white is you have the composite jack (Yellow cable) plugged into the luminance input on your TV's component inputs.
If a composite cable (yellow cable) is all that you have on hand right now, you need to make sure that it's plugged into the composite input on your television, and the composite output on your DVD player/game systems. Look for the yellow input and output, ignore the red, green, blue. But if you have component cables lying around somewhere and you want to use them, then you need to make sure those are plugged in accordingly as well (ignore the yellow input/outputs.)
As Alistair said you should buy cables online, either on eBay or an online retailer. Brick and mortar stores all seem to overprice cables ridiculously.
