Since the HDMI connection appears to work, let's look at the cable box to DVD recorder connection.

I think you mean component instead of RGB, right?

Did you check to see whether the buzzing is in one channel or both? You'll get a buzzing in one channel, the right channel, if you mistakenly plug the red video lead into an audio input. Since most component cable sets have red for red video and red for right channel, it's not impossible to switch them. If blue and green were reversed, you'd get a blue screen. Voila, your current setup.

Back up a bit and investigate your connection from the cable box to the DVD recorder. Plug in just green. You should get a black and white image. If the cable box's output scan rate is wrong, you'll get a blue screen or doubled-up image. Once you get black and white, add the red video lead, then the blue. You'll see the difference as you add the color leads. Note that green plus red leads give you green and red, green and blue leads give you green and blue, which doesn't make sense since green only gives you zero color.

Once you've got video, plug in the audio.