First of all, are you using a black and white TV? They made those once a upon a time, and if you're a kid maybe you have parents with an awesome sense of humor.
It sounds like you ruled out the game cartridge, so now isolate the issue to the console, cable or TV.
Plug your console into a different TV with the same cable to rule out your TV hardware.
Plug your console into the original TV using a different cable to rule out your cable.
Try a different type of cable (RF, composite, s-video), and if one of them gives color while the others dont, maybe you can work around the problem instead of fixing it.
If using an RF adapter, are you using the correct/same channel (3/4) on your TV and the RF box?
If you're using an S-video cable, maybe you're only getting luma and not chroma?
There should be 4 metal pins and one plastic guide tab in an s-video connector, check for those being bent/broken.
If SCART or import hardware... well I hope it's not an NTSC vs. PAL issue. Google for region-specific issues.