The best way to prevent the red rings of death is to buy the accessory fans that Microsoft recommends. It's interesting because Microsoft isn't affiliated with the makers of the fan, but they urge you to buy them. Anywho, to answer your question, the best thing to is to make sure you're not using the HD cables on a regular tv. I did it the first time I plugged in my 360 just because I wasn't savvy with the product. After you've determined that's not the problem, look into checking the plugs for rust or unnecessary bends or missing teeth. You'd be amazed how many bad cables Microsoft accidentally sends in their XBOX shipments.
If you still haven't determined the problem, you shoud try all new cables. I think they're warranted through the corporation within a year of purchase. Just send the old ones back, good or bad, and they'll shoot you a new set. And if you still haven't figured out what's wrong with it, then you need to seek professional i.e. nerd help.