I got my Xbox 360 back from the repair center today!
I forgot to post when it died, but it was the beginning of October. On October 1st I noticed some weird graphical anomalies during the final video of the Halo 3 campaign. On October 2nd I was getting the '3 red rings of death', and placed my support request over the phone.
A week later, on October 10th, I got the '360 coffin' to mail my unit back to the repair center in Texas.
I shipped it out on the 11th, and another week later on the 17th it arrived in Texas.
One additional week later, today the 25th, I received my repaired Xbox. It was the original one I had sent it, so it was a repair not a refurb replacement.
I am a little miffed that I missed out on the free Oblivion download, but at least I can start playing Portal finally.