It could be a bad cable, but more likely you need a signal amplifier. I have a Radio Shack in line amplifier on my TV out on the 721, and I get very good pictures all over the house, even through splitters. With only 1 TV and 1 50 foot run, you might also need an attenuater at the TV end of it, depending on if your signal has been over boosted or not. Alternately, you could buy an adjustable amplifier and turn it up until the grain goes away.
Do note that you will always introduce a certain amount of audible noise to the picture doing this. It will be at a very low level, and really you'd have to stand close to the TV with a black screen to hear it at all, but it is there. You won't hear it at all with normal viewing, but it is a reality that you can't amplify an already amplified video/audio signal without doing a little damage to the signal. This is because you are raising the noise floor of the signal, but it's better than a crappy picture.