So far, there has been little helpful advice in this topic. If it's 4 rings, plug in your AV cable. If it's 3 rings, hold the sync button and hit the eject button. The ring will have either 1,2,3, or 4 lights lit up. 4=0, 1=1, 2=2, 3=3. Hit the eject button 4 times and you get a 4 digit code. That code is the error code. Look it up
here (Scroll down a bit). Now depending on the code, you might be able to fix it. I bought my friend's RRoD'd xbox and got the error code 0102. This means that the thermal compound on the GPU and CPU isn't doing it's job (Microsoft got better thermal compound with the new ones). If you have a warranty, you could try sending it in. If not, it's very easy to fix. Follow the instructions
here to open your xbox and
here to fix the red ring.